Answer: The actual car length is 12ft.
Step-by-step explanation:
Actual car length = 3cm x 4ft/cm = 12ft
The percent of fat calories an American consumes each day is normally distributed withy mean of 36 and SD of about 10. Suppose a random sample of 20 Americans are chosen. Let X be the mean (average) percent of fat calories in the sample.
The percent of fat calories an American consumes each day is normally distributed with a mean of 36 and a standard deviation of about 10.
What is standard deviations?Standard deviation is a measure of the spread of a data set. It is calculated by taking the square root of the variance of the data set. It is a measure of how much the individual values in a data set are spread out from the mean. It is used to quantify the amount of variation or dispersion of a set of data values.
According to the Central Limit Theorem, the mean of the sample X will be normally distributed with a mean of 36 and a standard deviation of 10/sqrt(20). This means that the mean percent of fat calories in the sample will be normally distributed with a mean of 36 and a standard deviation of about 3.16. This means that 68% of the time, the mean percent of fat calories in the sample will be between 32.84 (36-3.16) and 39.16 (36+3.16), 95% of the time it will be between 29.68 (36-6.32) and 42.32 (36+6.32), and 99% of the time it will be between 26.52 (36-9.48) and 45.48 (36+9.48).
In other words, this is happening because the Central Limit Theorem states that the sample mean will be normally distributed, and that the standard deviation of the sample mean will be the standard deviation of the population divided by the square root of the sample size. By understanding this theorem, we can calculate the probability that the mean of the sample will fall within certain ranges.
In conclusion, the percent of fat calories an American consumes each day is normally distributed with a mean of 36 and a standard deviation of about 10. By understanding the Central Limit Theorem, we can calculate the probability that the mean of the sample will fall within certain ranges. This allows us to make predictions about the sample mean and helps us understand why this is happening.
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One leg of a right triangle is 3 inches shorter than the other leg. If the hypotenuse is 7
inches, what are the lengths of the legs? Give the exact answers, not decimal
approximations.
1/x is undefined for which real numbers?
Answer:
0
Step-by-step explanation:
Mai is jogging from her house to school. Her school is 2 5/6 miles from her house. She has gone 1 3/5 miles so far. How many miles does Mai still have to jog? Write your answer as a mixed number in simplest form.
Step-by-step explanation:
[tex]2 \times \frac{5}{6} = \frac{17}{6} [/tex]
[tex]1 \times \frac{3}{5} = \frac{8}{5} [/tex]
[tex] \frac{17}{6} - \frac{8}{5} [/tex]
[tex] \frac{17}{6} \times 5 = \frac{85}{30} [/tex]
[tex] \frac{8}{5} \times 6 = \frac{48}{30} [/tex]
[tex] \frac{85}{30} - \frac{48}{30} = \frac{37}{30} [/tex]
[tex]37 \div 30 = 7 \times \frac{1}{30} [/tex]
so 7 1/30
Enter the correct answer in the box.
What is the factored form of this expression?
x² + 6x-16
Substitute numerical values into the expression for p and q.
(0) 101
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d'º
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11
Vo 4
(x+p)(x+q)
<> ≤ 2
TT
aß
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sin cos tan sin-¹ cos¹ tan-¹
CSC sec cot log logo In
The calculated factored form of the expression x² + 6x - 16 is (x - 2)(x + 8)
What is the factored form of the expression?From the question, we have the following parameters that can be used in our computation:
x² + 6x - 16
Expand the expression
So, we have
x² + 6x - 16 = x² + 8x - 2x - 16
Factorize the expression
So, we have the following representation
x² + 6x - 16 = x(x + 8) - 2(x + 8)
Factor out x + 8
So, the expression becomes
x² + 6x - 16 = (x - 2)(x + 8)
Hence, the factored form of the expression x² + 6x - 16 is (x - 2)(x + 8)
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2.4.4 Quiz: Parabolas with Vertices Not at the Origin
The vertex of this parabola is at (2, -4). When the y-value is -3, the x-value is
-3. What is the coefficient of the squared term in the parabola's equation?
10
-10
OA. -1
B. 1
10-
C. 5
OD. -5
(2,-4)
10
Find the vertex and the axis of symmetry of the parabola given by the equation.
y = −x2 + 16x − 65
The axis of symmetry of the parabola is 8.
The vertex of the parabola is (8, -1).
How to find the vertex and the axis of symmetry of a parabola?The vertex of a parabola in standard form, y = ax² + bx + c, is given by:
Vertex, (h, k) = (-b/2a, c - b²/4a)
For y = -x² + 16x − 65:
a = -1, b = 16 and c = -65
-b/2a = -16/2(-1)
-b/2a = 8
c - b²/4a = -65 - (16)²/4(-1)
c - b²/4a = -65 + 64
c - b²/4a = -1
Vertex, (h, k) = (8, -1)
For a parabola in standard form, y = ax² + bx + c, the axis of symmetry of the parabola is given by:
x = -b/2a
For y = -x² + 16x − 65:
a = -1 and b = 16
Thus, the axis of symmetry of the parabola is:
x = -16/2(-1)
x = 8
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Circle O shown below has a radius of 8 inches. To the nearest tenth of an inch, determine the length of the arc, x, subtended by an angle of 74 .
The length of the arc, x, subtended by an angle of 74° in a circle with a radius of 8 inches is approximately 13.1 inches.
What is the central angle?A central angle is an angle with endpoints located on a circle's circumference and a vertex located at the circle's center (Rhoad et al. 1984, p. 420). A central angle in a circle determines an arc.
The length of an arc, x, subtended by an angle of 74° in a circle with a radius of 8 inches can be found using the formula:
x = (θ/360) × 2πr
where θ is the central angle in degrees, r is the radius of the circle, and π is the mathematical constant pi.
Substituting the given values, we get:x = (74/360) × 2π(8)
x ≈ 4.17π
To get the value to the nearest tenth of an inch, we can use the approximation π ≈ 3.14:
x ≈ 4.17 × 3.14
x ≈ 13.1
Therefore, the length of the arc, x, subtended by an angle of 74° in a circle with a radius of 8 inches is approximately 13.1 inches.
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7 of 7
Expand:
f(x)=x²-
DONE
+
1
Expanding the function expression f(x) = x^2 - 1, we get f(x) = (x - 1)(x + 1)
Expanding the function expressionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x^2 - 1
The above expression can be expanded using the difference of two squares
When this theorem is applied, we have
f(x) = (x - 1)(x + 1)
Hence, the function expression f(x) = x^2 - 1 when expanded is f(x) = (x - 1)(x + 1)
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Expanding the function expression f(x) = x^2 - 1, we get f(x) = (x - 1)(x + 1)
Expanding the function expressionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x^2 - 1
The above expression can be expanded using the difference of two squares
When this theorem is applied, we have
f(x) = (x - 1)(x + 1)
Hence, the function expression f(x) = x^2 - 1 when expanded is f(x) = (x - 1)(x + 1)
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In January, the amount of snowfall was 5 2/3 feet. In February, the amount of snowfall was 3 1/5 feet. What was the amount of snowfall in the two months combined? Write your answer as a mixed number in simplest form.
Answer:
Step-by-step explanation:
To add these fractions, we need a common denominator. The smallest common multiple of 3 and 5 is 15.
Converting 2/3 to fifteenths:
2/3 = 10/15
Converting 1/5 to fifteenths:
1/5 = 3/15
Now, we can add:
5 10/15 + 3 3/15 = 8 13/15
Therefore, the amount of snowfall in the two months combined was 8 13/15 feet.
ILL GIVE U BRAINLIST OR WHATEVER
The nationwide percentage of Americans who invest in the stock market is usually taken to be 55%. Is this percentage different in Georgia? A survey and analysis among Georgia residents led to a test statistic of 1.75.
(b) What is the p-value to test if the proportion of Georgians who invest in the stock market is different than the nationwide average? (Use 4 decimals.)
Okay, here are the steps to find the p-value:
1) The nationwide proportion of Americans who invest in the stock market is 55% (0.55)
2) The test statistic for Georgia is 1.75
3) To calculate the p-value, we need to know the degrees of freedom (df) and the critical value of the test statistic.
4) The df = 1, since we're comparing a single proportion (Georgia) to a fixed value (national average).
5) The critical value at df = 1 and 95% confidence is 3.84 (for a two-tailed test)
6) Since the test statistic of 1.75 is less than 3.84, we look up 1.75 in tables to find the p-value.
7) For a test statistic of 1.75 and df = 1, the p-value is 0.1860.
So the p-value to test if the proportion of Georgians who invest in the stock market is different than the nationwide average is 0.1860.
Let me know if you have any other questions!
Okay, here are the steps to find the p-value:
1) The nationwide proportion of Americans who invest in the stock market is 55% (0.55)
2) The test statistic for Georgia is 1.75
3) To calculate the p-value, we need to know the degrees of freedom (df) and the critical value of the test statistic.
4) The df = 1, since we're comparing a single proportion (Georgia) to a fixed value (national average).
5) The critical value at df = 1 and 95% confidence is 3.84 (for a two-tailed test)
6) Since the test statistic of 1.75 is less than 3.84, we look up 1.75 in tables to find the p-value.
7) For a test statistic of 1.75 and df = 1, the p-value is 0.1860.
So the p-value to test if the proportion of Georgians who invest in the stock market is different than the nationwide average is 0.1860.
Let me know if you have any other questions!
If 600 bolts were already examined and 12 were defective, determine the probability that next bolt found would be nondefective.
The probability that the next bolt found would be non-defective is 0.98 or 98%.
What is Probability Theory?A fundamental idea in mathematics and statistics, probability theory has several uses in the sciences, engineering, business, and social sciences. It is used to assess risks and uncertainties in diverse circumstances, analyse and forecast the possibility of events happening, and make decisions in the face of uncertainty.
Given:
Number of bolts already examined = 600
Number of defective bolts found = 12
Number of non-defective bolts = Total number of bolts examined - Number of defective bolts
= 600 - 12
= 588
Probability of finding a non-defective bolt = Number of non-defective bolts / Total number of bolts
= 588 / 600
= 0.98 or 98%
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Terry bought a new television set for $450. She paid nothing down but agreed to payments of $40.03 per month for 12 months. Find the annual percentage rate for the loan using the APR table
The annual percentage rate is%
The annual percentage rate for Terry's loan is 19.21%.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To find the annual percentage rate (APR) for Terry's loan, we can use the following formula:
APR = (2 × Monthly Payment ÷ Loan Amount) × (12 ÷ Loan Term in Months + 1)
First, we need to calculate the total amount Terry will pay for the TV over the 12-month period:
Total payments = Monthly payment × Loan term in months
Total payments = $40.03 × 12
Total payments = $480.36
Next, we can use the formula to calculate the APR:
APR = (2 × $40.03 ÷ $450) × (12 ÷ 12 + 1)
APR = (0.1774) × (1.0833)
APR = 0.1921 or 19.21%
Therefore, the annual percentage rate for Terry's loan is 19.21%.
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A net of a square pyramid is shown below.
What is the surface area, in square centimeters, of the pyramid?
Answer:
Option (B) 86.7 is the correct answer.
Step-by-step explanation :
Dividing the given diagram in 5 parts :
Firstly finding the area of one right angle triangle :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1}{2} \times b \times h}[/tex]
↠ b (base) = 5.1 cm↠ h (height) = 5.95 cmsubstituting all the given values in the formula :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1}{2} \times 5.1 \times 5.95}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1 \times 5.1 \times 5.95}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{5.1 \times 5.95}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{30.345}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = 15.1725\: {cm}^{2}}[/tex]
Hence, the area of right angle triangle is 15.1725 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Here we have 4 right angle triangle with equal base and height and we have already find the area of one right angle triangle. So, the area of 4 triangle will be :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = 15.1725 \: {cm}^{2}}[/tex]
[tex]\dashrightarrow\sf{Area \: of \: 4{(\triangle)} = 15.1725 \times 4}[/tex]
[tex]\dashrightarrow\sf{Area \: of \: 4{(\triangle)} = 60.69 \: {cm}^{2}}[/tex]
Hence, the area of 4 right angle triangles is 60.69 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Now, we have to find the area of square
[tex]\longrightarrow\sf{Area_{(Square)} = {a}^{2}}[/tex]
↠ a (side) = 5.1 cmSubstituting the given value in the formula :
[tex]\longrightarrow\sf{Area_{(Square)} = {(5.1)}^{2}}[/tex]
[tex]\longrightarrow\sf{Area_{(Square)} = {(5.1 \times 5.1)}}[/tex]
[tex]\longrightarrow\sf{Area_{(Square)} = 26.01 \: {cm}^{2}}[/tex]
Hence, the area of square is 26.01 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Now, calculating the total area :
[tex]{\sf{\implies{Total \: Area = Area_{(\triangle)} + Area_{(Square)}}}}[/tex]
↠ Area of triangle = 60.69 cm²↠ Area of square = 26.01 cm².[tex]{\sf{\implies{Total \: Area = 60.69 + 26.01}}}[/tex]
[tex]{\sf{\implies{Total \: Area = 86.7 \: {cm}^{2}}}}[/tex]
Hence, the total area of given diagram is 86.7 cm².
———————————————Answer:
Option (B) 86.7 is the correct answer.
Step-by-step explanation :
Dividing the given diagram in 5 parts :
Firstly finding the area of one right angle triangle :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1}{2} \times b \times h}[/tex]
↠ b (base) = 5.1 cm↠ h (height) = 5.95 cmsubstituting all the given values in the formula :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1}{2} \times 5.1 \times 5.95}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{1 \times 5.1 \times 5.95}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{5.1 \times 5.95}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = \dfrac{30.345}{2}}[/tex]
[tex]\dashrightarrow\sf{Area_{(\triangle)} = 15.1725\: {cm}^{2}}[/tex]
Hence, the area of right angle triangle is 15.1725 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Here we have 4 right angle triangle with equal base and height and we have already find the area of one right angle triangle. So, the area of 4 triangle will be :
[tex]\dashrightarrow\sf{Area_{(\triangle)} = 15.1725 \: {cm}^{2}}[/tex]
[tex]\dashrightarrow\sf{Area \: of \: 4{(\triangle)} = 15.1725 \times 4}[/tex]
[tex]\dashrightarrow\sf{Area \: of \: 4{(\triangle)} = 60.69 \: {cm}^{2}}[/tex]
Hence, the area of 4 right angle triangles is 60.69 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Now, we have to find the area of square
[tex]\longrightarrow\sf{Area_{(Square)} = {a}^{2}}[/tex]
↠ a (side) = 5.1 cmSubstituting the given value in the formula :
[tex]\longrightarrow\sf{Area_{(Square)} = {(5.1)}^{2}}[/tex]
[tex]\longrightarrow\sf{Area_{(Square)} = {(5.1 \times 5.1)}}[/tex]
[tex]\longrightarrow\sf{Area_{(Square)} = 26.01 \: {cm}^{2}}[/tex]
Hence, the area of square is 26.01 cm².
[tex]\begin{gathered} \end{gathered}[/tex]
Now, calculating the total area :
[tex]{\sf{\implies{Total \: Area = Area_{(\triangle)} + Area_{(Square)}}}}[/tex]
↠ Area of triangle = 60.69 cm²↠ Area of square = 26.01 cm².[tex]{\sf{\implies{Total \: Area = 60.69 + 26.01}}}[/tex]
[tex]{\sf{\implies{Total \: Area = 86.7 \: {cm}^{2}}}}[/tex]
Hence, the total area of given diagram is 86.7 cm².
———————————————Let ABC be any triangle .D is the midpoint of [BC]
1) Locate the points M, N and I such that :
MA+MB = 0
3NA+NC = 0
IM +2IN = 0
Answer:
We can use vectors to solve this problem. Let's assume that the position vector of point A is a, and the position vectors of points B and C are b and c respectively.
Since D is the midpoint of BC, we can find its position vector as:
d = (b + c)/2
Now, let's find the position vectors of M, N, and I using the given conditions:
MA + MB = 0
This means that the vector MA is equal in magnitude and opposite in direction to the vector MB. Since M is a point on the line segment AB, we can write:
MA = M - a
MB = M - b
So, MA + MB = 0 gives us:
M - a + M - b = 0
2M = a + b
M = (a + b)/2
Therefore, the position vector of M is:
m = (a + b)/2
Similarly, we can find the position vectors of N and I:
3NA + NC = 0
This means that the vector NA is three times the magnitude of the vector NC, and they are in opposite directions. Since N is a point on the line segment AC, we can write:
NA = N - a
NC = N - c
So, 3NA + NC = 0 gives us:
3(N - a) + (N - c) = 0
4N = 3a + c
N = (3a + c)/4
Therefore, the position vector of N is:
n = (3a + c)/4
IM + 2IN = 0
This means that the vector IM is twice the magnitude of the vector IN, and they are in opposite directions. Since I is a point on the line segment DM, we can write:
IM = I - m
IN = I - n
So, IM + 2IN = 0 gives us:
I - m + 2(I - n) = 0
3I = 2m + 2n
I = (2m + 2n)/3
Therefore, the position vector of I is:
i = (2m + 2n)/3
So, the points M, N, and I are located at:
M = (a + b)/2
N = (3a + c)/4
I = (2m + 2n)/3
where:
m = (a + b)/2
n = (3a + c)/4
PLEASE SOMEONE HELPP!!!!
i know that answer Is −12
8
1
but i need explain! 100points, plus 5 Stars+ brainliest
[tex] - 3 \frac{3}{4} - x = -6 \frac{1}{6} [/tex]
THIS IS MATH FOR 7TH GRADE!!
Answer:
[tex]x=2\frac{5}{12}[/tex]
Step-by-step explanation:
Given equation:
[tex]-3\frac{3}{4}-x=-6\frac{1}{6}[/tex]
Begin by adding x to both sides of the equation:
[tex]-3\frac{3}{4}-x+x=-6\frac{1}{6}+x[/tex]
[tex]-3\frac{3}{4}=-6\frac{1}{6}+x[/tex]
Add -6¹/₆ to both sides of the equation:
[tex]-3\frac{3}{4}+6\frac{1}{6}=-6\frac{1}{6}+x+6\frac{1}{6}[/tex]
[tex]-3\frac{3}{4}+6\frac{1}{6}=x[/tex]
Swap sides:
[tex]x=6\frac{1}{6}-3\frac{3}{4}[/tex]
Rewrite the mixed numbers as improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:
[tex]x=\dfrac{6 \times6+1}{6}-\dfrac{3 \times 4+3}{4}[/tex]
[tex]x=\dfrac{36+1}{6}-\dfrac{12+3}{4}[/tex]
[tex]x=\dfrac{37}{6}-\dfrac{15}{4}[/tex]
When subtracting fractions, we must ensure that they have the same denominator. To do this, find the least common multiple (LCM) of the two denominators.
As 6 and 4 are factors of 12, then 12 is the LCM.
Rewrite the fractions as their equivalent fractions (with a denominator of 12) by multiplying the numerator and denominator by the same number.
[tex]x=\dfrac{37\times 2}{6\times 2}-\dfrac{15\times3}{4\times3}[/tex]
[tex]x=\dfrac{74}{12}-\dfrac{45}{12}[/tex]
Now the fractions all have the same denominator, we can simply subtract the numerators:
[tex]x=\dfrac{74-45}{12}[/tex]
[tex]x=\dfrac{29}{12}[/tex]
Finally, convert the improper fraction into a mixed number:
[tex]x=\dfrac{24+5}{12}[/tex]
[tex]x=\dfrac{24}{12}+\dfrac{5}{12}[/tex]
[tex]x=2+\dfrac{5}{12}[/tex]
[tex]x=2\frac{5}{12}[/tex]
Which data set has the largest standard deviation
The biggest standard deviation belongs to B. 1,6,3,15,4,12,8. This is due to the fact that this data set's range of values is substantially wider than that of the other sets, which raises the standard deviation.
what does standard deviation mean?
In statistics, standard deviation is a measure of the amount of variability or dispersion in a set of data. It measures how spread out the data is from the mean or average value.
The standard deviation serves as a gauge for how widely dispersed from the mean a set of data is. It is calculated by averaging the squared deviations from the mean, or variance, which is the variance expressed as a square root. In statistics and probability theory, the standard deviation is frequently used to quantify the variability of a data collection. It is crucial to understand that standard deviation differs from a data set's range, which is only the difference between greatest and lowest values.
Because standard deviation accounts for all of the data points in the set, it is a more accurate statistic.
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Complete Question:
Which data set has the largest standard deviation
A.3,4,3,4,3,4,3
B.1,6,3,15,4,12,8
C. 20, 21,23,19,19,20,20
D.12,14,13,14,12,13,12
Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to at least 4 decimal places.
539=13^r+9
The solution for r is:
r = ln(539)/ln(13) - 9
And an estimation is:
r = -6.5478
How to solve the exponential equation?Remember the rule for logarithms of powers:
ln(x^n) = n*ln(x)
Now let's look at our equation, here we have:
539 = 13^(r + 9)
We want to solve this equation for r, to do so, we can apply the natural logarithm in both sides:
ln(539) = ln( 13^(r + 9))
Using the rule we can rewrite this as:
ln(539)= (r + 9)*ln(13)
Now just solve the equation for r:
r = ln(539)/ln(13) - 9
And an approximate solution is:
r = -6.5478
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1) Find AB
B
A 9 in
Use the Law of
Sines:
SinA
a
(0) 8 in
A
54°
11 in
D 7 in
5 in
SinB
b
12
31 in
SinC
C
Remember
Check the picture below.
[tex]\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(54^o)}{31}=\cfrac{\sin(12^o)}{AB}\implies AB\sin(54^o)=31\sin(12^o) \\\\\\ AB=\cfrac{31\sin(12^o)}{\sin(54^o)}\implies AB\approx 8~in[/tex]
Make sure your calculator is in Degree mode.
PLS HELP!! suppose a scatterplot is created from the points in the following table. when x=7, what is the second coordinate in a scatterplot of the linearized data? round the answer to the tenth place.
a. 0.8
b. 2.1
c. 54.3
d. 112.8
Answer:
D
Step-by-step explanation:
i think its D because next to x the y coordinate is 112.8
What is the meaning of "Since the angle from axis j to axis i is [tex]\pi (i-j)/n[/tex], it follows that [tex]s _{i}\circ s_{j}=r_{i-j}[/tex]?
This statement describes the relationship between symmetries and rotations
Explaining the meaning of the statement as statedIn this context, "axis i" and "axis j" refer to two different coordinate axes, and "n" is the total number of axes. The notation "s_i" represents a reflection transformation across axis i, and "r_k" represents a rotation transformation that rotates the entire coordinate system by an angle of 2πk/n, where k is an integer between 0 and n-1.
The statement "Since the angle from axis j to axis i is π(i-j)/n, it follows that s_i ∘ s_j = r_{i-j}" means that if we reflect the coordinate system across axis i, and then reflect it again across axis j, the resulting transformation is equivalent to rotating the entire coordinate system by an angle of 2π(i-j)/n. In other words, the composition of the two reflections is equivalent to a single rotation.
This relationship is important in the study of group theory and symmetry, where it is used to understand the properties of groups of transformations that preserve the symmetry of an object or system.
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An incoming freshman took her college’s placement exams in French and mathematics. In French, she scored 92 and in math 80. The overall results on the French exam had a mean of 72 and a standard deviation of 17, while the mean math score was 70, with a standard deviation of 8. What are the z-scores for the two subjects?
A. -1.18, and 1.25
B. 1.18, and -1.25
C. 8, and 17
D. 1.18, and 1.25
The z-scores of the two subjects are 1.18, and 1.25 respectively
Given data ,
The z-score is a measure of how many standard deviations a data point is away from the mean of a data set.
z = (X - μ) / σ
where X is the data point, μ is the mean, and σ is the standard deviation.
For the French exam:
X = 92 (score obtained by the student)
μ = 72 (mean of the French exam)
σ = 17 (standard deviation of the French exam)
On simplifying , we get
z_french = (92 - 72) / 17 = 1.18
For the math exam:
X = 80 (score obtained by the student)
μ = 70 (mean of the math exam)
σ = 8 (standard deviation of the math exam)
z_math = (80 - 70) / 8 = 1.25
Hence , the z-scores are calculated
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Compound interest on a certain sum of money for 2 years is Rs.2600 while the simple interest on the same sum for the same time period is Rs.2500. Find the rate of interest.
13.5%
15%
12.8%
8%
The rate of interest according to the given data is 12.8%.
To answer this problem, we may utilize the compound interest formula:
A = P(1 + r/n)^(nt)
where A denotes the ultimate amount, P the principle, r the yearly interest rate, n the number of times the interest is compounded each year, and t the period in years.
We know that the compound interest on a certain payment over two years is Rs. 2600. Let us refer to the principal as P. Then we may type:
2600 = P(1 + r/100)^2 - P
When we simplify this equation, we get:
2600 = P[(1 + r/100)^2 - 1]
Dividing both sides by P[(1 + r/100)^2 - 1], we get:
1 = 1/[(1 + r/100)^2 - 1]
Simplifying even further, we get:
1 + (1 + r/100)^2 - 1 = (1 + r/100)^2
Taking the square root of both sides yields:
1 + r/100 = 1 + sqrt(2600/2500)
1 + r/100 = 1 + 0.04
r/100 = 0.04
r = 4%
As a result, the yearly interest rate is 4%. This, however, is the basic interest rate. To get the compound interest rate, use the following formula:
CI = P(1 + r/100)^2 - P
2500 = P(1 + 4/100)^2 - P
Simplifying this equation, we get:
2500 = P(1.04^2 - 1)
2500 = P(0.0816)
P = 30637.25
So the principal is Rs. 30637.25, and the annual compound interest rate is:
r = 100[(30637.25/10000)^(1/2) - 1]
r = 12.8%
Therefore, the rate of interest is 12.8% (rounded off to one decimal place).
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What is mHI?
mHI
I
=
H
O
120°
120°
J
The calculated value of the measure of the arc HI is 55 degrees
Calculating the measure of the arc HIFrom the question, we have the following parameters that can be used in our computation:
The circle
The sum of angles at a point is 360
So, we have
∠HAI + 60 + 100 + 145 = 360
When the like terms are evaluated, we have
∠HAI = 55
The angle subtended by the arc equals the angle at the center
This means that
mHI = ∠HAI
By substitution, we have
mHI = 55 degrees
Hence, the arc HI is 55 degrees
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what is the equation that represents the linear function f for the points (1,2) and (4,1)
Answer: f(x)= -0.333x + 2,333
Please help me figure this out, im not sure how i should be doing this
The table for the population of the colony at the different times of the study is found.
Explain about the exponential function:Calculating the exponential growth as well as decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for illustration, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, as well as disease spread.
Given functions are-
P(t) = 9.[tex](1.02)^{t}[/tex]
Q(t) = 9.[tex]e^{0.02t}[/tex]
Population is estimated in thousands.
Table for the population of the colony:
t (time in months) P(t) = 9.[tex](1.02)^{t}[/tex] Q(t) = 9.[tex]e^{0.02t}[/tex]
6 P(6) = 9.[tex](1.02)^{6}[/tex] = 10.13 Q(t) = 9.[tex]e^{0.02*6}[/tex]= 10.14
12 P(12) = 9.[tex](1.02)^{12}[/tex] = 11.41 Q(t) = 9.[tex]e^{0.02*12}[/tex] = 11.44
24 P(24) = 9.[tex](1.02)^{24}[/tex] = 38.60 Q(t) = 9.[tex]e^{0.02*24}[/tex] = 14.54
48 P(48) = 9.[tex](1.02)^{48}[/tex]= 23.28 Q(t) = 9.[tex]e^{0.02*48}[/tex]= 23.50
100 P(100) = 9.[tex](1.02)^{100}[/tex] = 65.20 Q(t) = 9.[tex]e^{0.02*100}[/tex]= 66.50
Thus, the table for the population of the colony at the different times of the study is found.
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C =5/9 × (F – 32) What is the answer
Answer:
c
=
5
9
⋅
(
f
−
32
)
Rewrite the equation as
5
9
⋅
(
f
−
32
)
=
c
.
5
9
⋅
(
f
−
32
)
=
c
Multiply both sides of the equation by
9
5
.
9
5
(
5
9
⋅
(
f
−
32
)
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=
9
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c
Simplify both sides of the equation.
Tap for more steps...
f
−
32
=
9
c
5
Add
32
to both sides of the equation.
f
=
9
c
5
+
32
Please help me im struggling with my test
The y-intercept is (0, 10) and the values of x that make sense are x > 0
The graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = 10(2)^x
The graph is added as an attachment
The y-interceptThis is the point of intersection with the y-axis
From the graph, it is (0, 10)
The values of x that make senseThese are the values whose corresponding y values are not negative
In other words, the values are x > 0
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Let x = 7/8 and y = -2/9. If x * z = y, then what is z?
Will mark brainiest for good and real answers only!
Vector C is 3.5 units West and Vector D is 3.3 units South. Vector R is equal to Vector D - Vector C. Which of the following describes Vector R?
8.3 units 54
South of East
8.3 units 54circ South of East
4.8 units 47
East of South
4.8 units 47circ East of South
6.2 units 32
West of South
6.2 units 32circ West of South
5.9 units 52
South of West
The corresponding to Vector R is 4.8 units 47 East of South 4.8 units 47circ East of South
How to solve for the vectorVector C comprises a magnitude of -3.5i
Vector D is established as –3.3j (South bearing is thought to be negative along the y-axis).
Vector R = Vector D - Vector C
= (-3.3j) - (-3.5i)
= 3.5i - 3.3j
To evaluate the strength of Vector R, we must first compute its magnitude:
Magnitude of R = √((3.5)^2 + (-3.3)^2) ≈ 4.8 units.
determine the direction,
we shall need to calculate the angle θ with respect to the South direction (the negative y-axis):
tan(θ) = (3.5) / (3.3);
θ = arctan(3.5 / 3.3) ≈ 47°
Hence the answer is option 2
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