Answer:
The radius is 4.
Step-by-step explanation:
Concepts:
Diameter is usually defined as a straight line passing through the center of a circle or sphere and meeting the circumference or circle at each end.Radius is usually defined as a straight line extending from the center of a circle or sphere to the circumference of surface. (Half of diameter).To figure this out:
R = 1/2 d
R = 1/2 8
R = 4
A study of a local high school tried to determine the mean amount of money that each
student had saved. The study surveyed a random sample of 69 students in the high
school and found a mean savings of 5000 dollars with a standard deviation of 1400
dollars. At the 95% confidence level, find the margin of error for the mean, rounding
to the nearest whole number. (Do not write ).
Using the t-distribution, it is found that the margin of error for the 95% confidence interval is of $336.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The margin of error is given by:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 69 - 1 = 68 df, is t = 1.9955.
The standard deviation and sample size are given, respectively, by:
s = 1400, n = 69.
Hence, the margin of error in dollars is given by:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
[tex]M = 1.9955\frac{1400}{\sqrt{69}}[/tex]
M = 336.
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At the end of every month, Katie saves 20 percent of her take home pay after her taxes. If Katie is taxed at a 25 percent tax rate, which of the following expressions represents Katie’s total savings at the end of six months? A. 0.9S B. 1.5S C. 2.2S D. 2.8S
The correct answer is option A which is the expression will be 0.9S.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
At the end of every month, Katie saves 20 percent of her take-home pay after her taxes. If Katie is taxed at a 25 percent tax rate,
The expression of the salary after six months will be calculated as:-
Let the gross salary is S
The net salary will be = 0.75S
Savings will be = 0.75 x 0.20 S = 0.15S
After six months the savings will be:-
Savings = 0.15 x 6 S
Savings = 0.9S.
Therefore the correct answer is option A which is the expression will be 0.9S.
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What type of triangle has only two congruent sides?
Answer: A triangle that only has two congruent sides is called an isosceles triangle. Two equal sides and two equal angles.
please help i need to turn this in!!!
Answer:
a. $3150
b. $3307.50, $3472.875
c. B(n) = 3000(1.05)^t
Step-by-step explanation:
just a disclaimer i havent done interest in a while so this might not be right
also im assuming this is compound interest
a. P = original amount; r = interest percentage, x = amount of total money
x = P(1 + (r/100)) = 3000(1 + 0.05) = 3150
b. x = 3000(1.05)^2,3 = 3307.5, 3472.875
c. B(n) = P(1+(r/100)^t for t in years. plug in the values to get B(n) = 3000(1.05)^t
Factor higher degree polynomials
(x^2 - 4) (x^2 + 6x + 9)
[tex]~~~(x^2 -4)(x^2 +6x +9)\\\\=(x^2 -2^2)(x^2 +2 \cdot 3x +3^2)\\\\=(x+2)(x-2)(x+3)^2[/tex]
If the simple interest on $4000 for 2 years is $400, then what is the interest rate?
Step-by-step explanation:
the answer is 5 percentage because the formula is 100 * 400 over 4000 * 2
19 Which figure(s) below can have a triangle as a two-dimensional cross
section?
I. cone
II. cylinder
III. cube
IV. square pyramid
(1) I, only
(2) IV, only
(3) I, II, and IV, only
(4) I, III, and IV, only
The figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only
How to determine the figures?The cross-section of three-dimensional figures are as a result of slicing the figure along its axis.
When the cube is sliced with its plane, it gives a triangle faceWhen a cone is sliced vertically, it gives a triangle faceOne of the faces of a square pyramid is a triangle; so it has a triangle faceHence, the figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only
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A group surveyed a mix of people below and above 40 years old about whether or not they visit a dentist once a year. This table gives the survey results.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 8 22
Above 40 17 13
Which table shows the relative frequency of people above 40 years old who do not visit a dentist once a year? Round your answers to the nearest hundredth.
A.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.32 0.68
Above 40 0.63 0.37
B.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.35 0.65
Above 40 0.68 0.32
C.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.37 0.63
Above 40 0.53 0.47
D.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.27 0.73
Above 40 0.57 0.43
The frequency table that shows the relative frequency of people older than 40 and don't visit the dentist is:
D. Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.27 0.73
Above 40 0.57 0.43
What is the relative frequency required?The relative frequency of those older than 40 and don't go annually to a dentist can be found as:
= Number of over 40 who don't go to dentist / Total of those over 40 surveyed
Solving gives:
= 13 / (17 + 13)
= 13 / 30
= 0.43
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Answer:
Its D, I got it right on a test :)
Step-by-step explanation:
Greg deposited $4000 into an account with a 9.8% annual interest rate, compounded semiannually. Assuming that no withdrawals are made, how long will it
take for the investment to grow to $4616?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
The number of years it would take $4000 to grow to $4616 is 2.92 years.
How many years would it take the investment to have a value of $4616?When an amount earns compound interest compounded semi annually, it means that both the amount invested and the interest accrued increases in value twice yearly.
Number of years = (In FV / PV) / r
r = 9.8/2 = 4.90%FV = future value = 4616PV = present value = 4000(In 4616 / 4000) / 0.049 = 2.92 years
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help me with this problem please i’m confused
Answer:
3rd
Step-by-step explanation:
If you know about linear eq. it's just a simple rule no worry
pls help plsssssssssssssssssssssssssssssssssssssssssss ASAP
If Mr. Price adds two more CDs that are 38 minutes and 40 minutes, the third quartile would increase.
What is the impact of adding two more CDs?A box plot is used to study the distribution and level of a set of scores. The two whiskers represent the minimum and maximum value.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
When the two CDs are added, the median would decrease. The first quartile and the third quartile would increase. The interquartile range would increase.
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The athlete jogged a distance of 4850 yards in 20 minutes. What is the time needed to cover 9215 yards at the same rate?
Equation:
Answer
Answer:
38 minutes
Step-by-step explanation:
Yards covered in a minute = 4850/20 = 242.5
Time needed to cover 9215 yards = 9215/242.5 = 38 min
Rice Yield = 600 - 2.05 * Maximum Temperature, R-Squared = 0.05, Standard Error of Regression = 11.5.
(a) What is the interpretation on the coefficient on Maximum Tem perature in this regression? (2 Marks)
(b) If Average Maximum Temperature in a district during the growing season is 25◦C, what is the annual rice yield in that district? (1 Mark)
(c) How do you interpret the R-Squared coefficient in this regression? (1 Mark)
(d) A district had an Average Maximum Temperature during the growing season of 25◦C , and suppose it increased to 30◦C, What is the regression’s prediction for the change in this district’s Yearly Rice Yield? (1 Mark)
Answer:
Calculate it you will now the answer and im elementery school
(8.2 x 10^4) + (9.7 x 10^5)
Answer:
1.052 × 10⁶
Step-by-step explanation:
82,000 + 970,000 = 1,052,000
Answer:
[tex]\left(8.2\cdot \:10^4\right)+\left(9.7\cdot \:10^5\right)=1,052,000[/tex]
Step-by-step explanation:
[tex]\left(8.2\cdot \:10^4\right)+\left(9.7\cdot \:10^5\right)\\=8.2\cdot \:10^4+9.7\cdot \:10^5\\\\\rightarrow 10^4 = 10000\\= 8.2 \cdot 10000\\= 82000\\\rightarrow 10^5 = 100000\\= 9.7 \cdot 100000\\= 970000[/tex]
[tex]970000 + 82000 = 1052000[/tex]
Kenzie makes quilts from blue and purple pieces of fabric. The diagram shows the ratio of blue pieces to
purple pieces.
Blue pieces
Purple pieces
The table shows the number of purple pieces and the number of total pieces that Kenzie will make on two
of her quilts.
Based on the ratio, complete the missing values in the table.
Quilt Purple pieces Total pieces
A
56
B
20
The purple pieces are 35 and total pieces is 32 if the Kenzie makes quilts from blue and purple pieces of fabric.
What is the ratio?
It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
The question is incomplete.
The complete question is in the picture, please refer to the picture.
Total number of pieces = 3+5 = 8
So, the purple pieces = 5(5/8) = 35
Total pieces = 20/(5/8) = 4×8 = 32
Thus, the purple pieces are 35 and total pieces is 32 if the Kenzie makes quilts from blue and purple pieces of fabric.
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Find the minimum distance between the point (-3,2) and the line y = -x + 1
(Enter an exact answer with a square root.)
The minimum distance between the point(-3,2) and the line y = -x + 1 is [tex]\sqrt{2}[/tex] units.
What is a line segment?The line that joins two points on a cartesian plane is a line segment.
Analysis:
The formula for calculating distance between a line and a point is
d = [tex]\frac{Ax1 + By1 + c}{\sqrt{A^{2} + B^{2} } }[/tex]
where A = coefficient of x term of the line, B = coefficient of y in the line and C is the constant term of the line.
x1 and y1 are coordinates of the point.
for the line y = -x + 1 which is = y + x -1 = 0, A = 1, B = 1, C = -1, x1 = -3, y = 2
d = [tex]\frac{1(-3) + 1(2) + (-1)}{\sqrt{(-3)^{2} + 2^{2} } }[/tex]= [tex]\sqrt{2}[/tex] units
In conclusion, the distance between the point and the line is [tex]\sqrt{2}[/tex] units
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P(A1) = .20, P(A2) = .40, P(A3) = .40, P(B1 | A1) = .25, P(B1 | A2) = .05, and P(B1 | A3) = .10. Use Bayes’ theorem to determine P(A3 | B1).
Answer:The result follows from manipulating the conditional probability. By definition,
By the law of total probability,
So we have
Step-by-step explanation:
P(A|B) = P(B|A)×P(A)/P(B)
so, in our case
P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/P(B1)
I assume that the problem definition means that A1, A2, A3 are independent and not overlapping events (hence their sum is 1). and therefore, B1 can only happen after A1 or after A2 or after A3. there is no other possibility for B1 to happen.
so,
P(B1) = P(B1|A1) + P(B1|A2) + P(B1|A3) =
= 0.25 + 0.05 + 0.1 = 0.4
therefore,
P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/0.4 = 0.1
Which steps are needed to solve this equation?
.
b + 6 = 21
Answer:
15
Step-by-step explanation:
Isolate the b by subtracting 6 from both sides
Question: b + 6 = 21
Subtract 6 from both sides
b + 6 - 6 = 21 - 6
b = 15
Answer:b=15
Step-by-step explanation:
Just subtract 6 from 21 to get b.
Which statement correctly compares the function shown on
this graph with the function y = 4x + 2?
how do I Simplify 4+9x2÷3-1
Step-by-step explanation:
Step 1: Simplify
[tex]4+9x^2/3 - 1[/tex]
[tex]=4+3x^2+-1[/tex]
Step 2: Combine Like Terms:
[tex]= 4+3x^2+1-1[/tex]
[tex]= (3x^2)+(4+-1)[/tex]
Answer: [tex]= 3x^2+3[/tex]
Explanation in words (Short Form)
- The first step is to use the formula and simplify it. So first we will Rewrite the division as a fraction.
- The second step is to Cancel the common factor of 9 and 3. Then Factor 3 out of 3. After that Cancel the common factor.
- The third step is to divide [tex]3x^2[/tex] by 1. Then at the end, subtract 1 from 4. The answer will result as [tex]3x^2+3[/tex]
Answer:
[tex]=3x^2+3[/tex]
Hope this helps.
Fabian took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4.80 plus $4 per mile. The total fare was $44.80, not including the tip. How many miles was the taxi ride?
Answer:
10 miles
Step-by-step explanation:
total amount=$44.80
pick up fee=$4.80+$4 per mile
to get the miles of the taxi ride it will be=total amount-pick up fee÷$4
$44.80-$4.80÷$4
$40÷$4
=10 miles
THANK YOU
multiply: (a+b),(a+b) and (a+b)
Answer:
Here,
[tex](a + b) [(a + b)(a + b)][/tex]
[tex](a + b)( {a}^{2} + 2ab + {b}^{2} )[/tex]
[tex]a( {a}^{2} + 2ab + {b}^{2} ) + b( {a}^{2} + 2ab + {b}^{2} )[/tex]
[tex] {a}^{3} + {2a}^{2} b + {ab}^{2} + {a}^{2} b + {2ab}^{2} + {b}^{3} [/tex]
[tex] {a}^{3} + 3 {a}^{2} b + {3ab}^{2} + {b}^{3} [/tex]
Thus,[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]
Thus, in case of multiplication of a binomial or a trinomial by a binomial or a trinomial each term of the binomial or the trinomial should multiply each term of the given binomial or the trinomial and if needed, simplification should be performed.
Maya invested $2,100 in an account paying an interest rate of 7\tfrac{3}{8}7 8 3 % compounded continuously. Jack invested $2,100 in an account paying an interest rate of 7\tfrac{5}{8}7 8 5 % compounded monthly. After 12 years, how much more money would Jack have in his account than Maya, to the nearest dollar?
This are interest added on a sum of money invested. Jack will have $168.95 more than Maya in his account
Compound interestThis are interest added on a sum of money invested. The formula for calculating compound amount is given as;
A = P(1 +r/n)^nt
Given the following parameter
P =$2100
rate r = 7 5/8% = 0.07625
time t = 12 years
n =12 (monthly)
Substitute
A = 1200(1+0.07625/12)^12(12)
A = 1200 (2.4895)
A = $2987.46
For Maya
A = 1200(1+0.07375)^12
A = 2818.50
Take the difference
Difference =$2987.46 - $ 2818.5
Difference = $168.95
Hence Jack will have $168.95 more than Maya in his account
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In which table does yvary directly with x?
The table in which y varies directly with x is table C.
What is direct variation?
When a variable varies directly with another variable, it means that as one variable increases, the other variable also increases.
The equation that is used to represent direct variation is:
y = kx
Where y is the constant of proportionality
In table c, k is equal to 26
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in the figure, angle D measures 31° and angle A measures 27
The measurement of angle B Is ?The measurement of angle F is?
The acute angles of a right triangle are complementary, so:
[tex]m\angle B=90-27=\boxed{63^{\circ}}\\m\angle F=90-31=\boxed{59^{\circ}}[/tex]
Can someone solve this eq (integration)
I did it but the answer I got is different to what my textbook says
Answer:
I hope you can help
The definition of a circle uses the undefined term _______.
O arc
O line
O plane
O ray
Answer:
The correct answer is:
Plane.
Step-by-step explanation: There are three terms generally considered to be undefined in geometry: point, line and plane.
A circle is the set of all points in a plane the same distance from a given point called the center. The only of our options that is used in this definition is
The correct answer is;
⇒ Plane.
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Since, We know that;
There are three terms generally considered to be undefined in geometry: point, line and plane.
Hence, A circle is the set of all points in a plane the same distance from a given point called the center.
And, The only of our options that is used in this definition is plane.
Thus, The correct answer is;
⇒ Plane.
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Please help me solve the x and y values in thes simultaneous equation;
Answer:
x = 3 or x = 1
y = 3 or y = -1
(x, y) = (3, 3)
(x, y) = (1, -1)
Step-by-step explanation:
A class sold tickets to their school play. Each of the 232323 students in the class sold 444 tickets. The cost of each ticket was \$7$7dollar sign, 7.
How much money did the class earn by selling tickets to the play?
\$
Answer:
the class earned $722059884
Step-by-step explanation:
because each person sold 444 tickets and there was 232323 students
=232323×444
=103151412
because 103151412 tickets were sold and a ticket cost $7
=103151412×7
=722059884
The diameter of a circle is 94 cm.
By first calculating the radius, work
out the area of the circle.
2
Give your answer in cm² to 1 d.p.
[tex]\huge\boxed{Formula: r= \frac{d}{2}}[/tex]
Substitute the values according to the formula.
[tex]r=\frac{94}{2}[/tex]
[tex]\large\boxed{r=47 \: cm}[/tex]
Now, let's find the area.
[tex]\huge\boxed{Formula:a= \pi{r}^{2}}[/tex]
So, we'll have to multiply π, 47 and 47.
Substitute the values according to the formula.
[tex]a= \pi{47}^{2}[/tex]
[tex]a= 6939.778172 \: {cm}^{2}[/tex]
[tex]\large\boxed{a= 6939.8 \: {cm}^{2}(1 \: d.p)}[/tex]
Hence, the area of the given circle is 6939.8 square centimeters.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the radius & area of the circle.
To find the [tex]\star\bf{radius}\star[/tex], we divide the diameter by 2:
[tex]\star~\bf{94\div2}[/tex]
[tex]\star~\bf{Radius=47}\star[/tex]
Now that we have the radius, let's compute the area! :)
///\\\///\\\///\\\///\\\///\\\////\\\///\\///\\\///\\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\//\\\//\\
Calculating the Area
We can work out the area of a circle by using this formula:
[tex]\star\boxed{\pmb{A_{(circle)}=\pi r^2}}\star[/tex]
Where
[tex]\dag[/tex] A=Area of a circle
[tex]\dag[/tex] [tex]\pi =3.14...[/tex]
[tex]\dag[/tex] r=radius
Have you noticed the [tex]\large\pmb{^2}[/tex] next to r? This tells us that we should multiply the radius times itself.
Now it's time to substitute the values:
[tex]\star~\large\pmb{A=3.14\times47^{2}}\star[/tex]
Let's simplify it. The acronym PEMDAS will help us, and we won't make any mistakes in the Order of Operations! :)
Here's what it stands for:
P=Parentheses
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
2 is an exponent.
So what do you think we should do first?
[tex]\square[/tex] Square 47.
[tex]\square[/tex] Multiply 3.14 times 47 and then square.
That's right, we should square 47 first. :)
[tex]\star~\large\pmb{A=\pi \times2209}}\star[/tex]
Now, according to PEMDAS, we should multiply pi times 2209; after multiplying, we obtain:
[tex]\star~\large\pmb{A=6936.8\:cm^2}\star[/tex]
Remember, the area of any shape is measured in units squared.
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{\bf{The\;area\;of\;any\;shape\;is\;measured\;in\;units\;squared}}[/tex]
Hope this helps you out! :D
Ask in comments if any queries arise.
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[tex]\bigstar\footnotesize\pmb{M^ar_ib^el\;Peri}[/tex]