Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10.
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
A fish detects vibrations in the water around it by means of its lateral lines, rows of sensory receptors along each side of the body. Based on what you know about sensory receptors, the lateral line receptors are probably
A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it. The lateral line receptors are most likely is Mechanoreceptors.
Given that,
A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it.
We have to find according to your understanding of sensory receptors, the lateral line receptors are most likely is.
We know that,
A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it. According to your understanding of sensory receptors, the lateral line receptors are most likely is Mechanoreceptors.
What is Mechanoreceptor?Mechanoreceptors, also known as Mechanoreceptors, are specialized neurons that react to pressure and deformation caused by mechanical forces. They are surrounded by sensory neurons, which translate external pressure into electrical signals that are sent to the brain.
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is 0 a solution for w+3=w
Answer:No
Step-by-step explanation:
0+3 = 3, not zero
an online magazine allows you to view up to 25 articles free to view 30articles, you pay $49.15. to view 33 articles, you pay $57.40. what is the cost of each article for which you pay a fee?
Answer:
$2.75
Step-by-step explanation:
The difference in cost for 33 articles and 30 articles is
$57.40 - $49.15 = $8.25
From 30 to 33 articles, the difference is 3 articles.
3 articles cost $8.25.
Cost per article = $8.25/3 = $2.75
Three groups of research participants have played a game with various amounts of violence and were assessed on a stress-related scale (where 0 = no stress, 100 = very stressed) afterwards. The first group of participants (Group 1) have played a non-violent game. The second group of participants (Group 2) have played a moderately violent game. The third group of participants (Group 3) have played a very violent game. The researchers would like to know if the results on a stress scale differ for these groups. What is the null hypothesis? (2 points) Your answer: What is the research hypothesis?
Since, F value is =19.056 is greater than F critical value =3.3541
Therefore, We have enough evidence that null hypothesis is not rejected
What is hypothesis ?A hypothesis is a theory that is put up to account for a phenomenon. Unless it can be tested through the scientific method, a hypothesis cannot be referred to as a scientific hypothesis. Scientific theories frequently begin with historical observations that cannot currently be fully explained by existing knowledge.
Here,
Null hypothesis,
[tex]H_{0}[/tex]: u1 = u2 =u3
u1,u2,u3 are means of stress scale for group 1 , group 2 and group 3
Alternate hypothesis,
[tex]H_{A}[/tex] : u1≠u2
The F value is =19.056
Using F critical value α=0.05
df numerator =2 , df denominator = 27
F critical value =3.3541
Conclusion : F value is =19.056 is greater than F critical value =3.3541
Therefore, We have enough evidence that null hypothesis is not rejected
We, conclude that all three groups are equals in terms of mean.
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You are packing books into a box. The box can hold at most 10 books. The function y=5.2x represent the weight y (in pounds) of x books
This question doesn't seem completed to me. Is there anything more after this?
The line of best fit is given as y = -5 - 8x. Find the value of y when x = 4.
Answer:
y = -37
Step-by-step explanation:
y = -5 - 8x
y = -5 - 8(4)
y = -5 + ( - 8 x 4 )
y = -5 + ( - 32)
y = -37
Match each expression on the left with its quotient. Use number sense and estimation to help.
5.85369.421.5
40.42 ÷ 4.3
15.48 ÷ 0.72
86.4 ÷ 2.4
50.31 ÷ 8.6
Answer:
5.85369.421.5 does not have a quotient because it is not a mathematical expression.
40.42 ÷ 4.3 = 9.4
15.48 ÷ 0.72 = 21.4
86.4 ÷ 2.4 = 36.0
50.31 ÷ 8.6 = 5.84
Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By = C.
(3,4) and (2,1)
Answer:
-3x+y=-5
Step-by-step explanation:
First, find the slope of the equation:
m=(y2-y1)/(x2-x1) ==> m=slope of equation
(x1, y1), (x2, y2) ==> (x1=3, y1=4), (x2=2, y2=1)
m=(1-4)/(2-3) ==> plugin x1=3, y1=4, x2=2, and y2=1
m=-3/(-1)
m=3
y=mx+b ==> slope-intercept equation
1=3(2)+b ==> plugin 3 for m and (2, 1) where x=2 and y=1
1=6+b ==> solve for b
1-6=6-6+b
b=-5
y=3x+(-5) ==> plugin -3 for m and -5 for b
y=3x-5 ==> simplify
Now, Isolate -5 since it is the only constant
y-3x=3x-3x-5 ==> isolate -5 by subtracting 3x on both sides
-3x+y=-5 ==> simplify and put in Ax+By=C form
y = 3x - 5
sorry can't help with step to step explanation......
Answer the question below and for part B write the equation with the answer that you get for part A.
A
B
C
D
From the linear function, the rate of change is 35 and the unit cost is 35
Linear FunctionA linear function is defined as a function that has either one or two variables without exponents.
In this problem, we have to write a linear function that models the table given. This will take the form of y = mx + c
m = slope or rate of change and c = constant or unit cost of the product.
The formula of slope of a line is given as
m = y₂ - y₁ / x₂ - x₁
Taking two points from the table;
m = 215 - 180 / 5 - 4
m = 35
Using the slope of the line, we can find the y - intercept of the function.
y = mx + c
215 = 35(5) + c
215 = 175 + c
c = 215 - 175
c = 40
The linear function of the table is y = 35x + 40
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In Exercises 1-3, decide whether enough information is given to prove that the triangles are congruent using either the SSS Congruence Theorem (Theorem 5.8) or the HL Congruence Theorem (Theorem 5.9). Explain.
1. The triangles are congruent based on the SSS congruence theorem.
2. The information is not enough.
3. Both are congruent by the HL congruence theorem.
What is the HL Congruence Theorem?If two triangles have a pair of congruent hypotenuses and a pair of congruent legs, then both triangles ae congruent to each other based on the HL congruence theorem.
What is the SSS Congruence Theorem?The SSS Congruence Theorem states that if any two triangles have three pairs of corresponding sides that are congruent to each other, then the triangles are congruent.
1. Based on the SSS congruence theorem, the pair of angles in figure 1 are congruent.
2. There is no information available that shows the triangles have a pair of congruent hypotenuses, nor have three pairs of corresponding congruent sides. Th information given is not enough to prove that they are congruent by SSS or HL.
3. Based on the HL congruence theorem,, they are congruent to each other.
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help Me out and I’ll give you brainliest
Answer: 5/8
Step-by-step explanation: There are 8 members. Out of 8, there are 5 people's weight that are higher than 135. Therefore the answer is 5/8.
Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples. Use a significance level of α = 0.01
Sample 1: n1 = 13, ¯x1 = 23, s1 = 6
Sample 2: n2 = 16, ¯x2 = 29, s2 = 5.9
(a) The degree of freedom is _____
(b) The test statistic is _____
(c) Determine the rejection region for the test of H0:μ1−μ2=0 and Ha:μ1−μ2≠0
(d) |t| > _____
To test the claim that the two samples described come from populations with the same mean, we can use a two-sample t-test.
(a) The degree of freedom is 27
(b) The test statistic is -2.67
(c) Determine the rejection region for the test of H0:μ1−μ2=0 and Ha:μ1−μ2≠0 : we do not reject the null hypothesis.
(d) |t| > 2.70
(1) The degree of freedom for the two-sample t-test is calculated as
df = n1 + n2 - 2 = 13 + 16 - 2 = 27.(2) The test statistic for the two-sample t-test is calculated as:
t = (¯x1 - ¯x2) / sqrt[(s1^2 / n1) + (s2^2 / n2)]Plugging in the values, we get:
t = (23 - 29) / sqrt[(6^2 / 13) + (5.9^2 / 16)] = -6 / sqrt[(36/13) + (34.81/16)] = -6 / sqrt[2.77 + 2.18] = -6 / sqrt[4.95] = -6 / 2.23 = -2.67(3) To determine the rejection region for the test, we can use a significance level of α = 0.01. For a two-tailed test with α = 0.01, the critical value for t is approximately 2.70. Since our test statistic (-2.67) is less than the critical value, we do not reject the null hypothesis.
(4) For the rejection region, we need to consider values of t that are either greater than or less than the critical value. Therefore, we need to consider |t| values that are greater than 2.70. |t| > 2.70.
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Sara needs to determine the number of 3/4 pound servings into 9 3/4 pounds of turkey.she calculates that there are 13 servings.is stated calculation correct why or why not
There are 9.75 servings, not 13 servings.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
the number of 3/4 pound servings in pounds of turkey
she calculates that there are 13 servings.
so,
9 (3/4) = (36 + 3) /4
= 39/4
= 9.75
Hence, there are 9.75 servings, not 13 servings.
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HELP URGENT
A set of data items is normally distributed with a mean of 200 and a standard deviation of 40. Find the data item in this
distribution that corresponds to the given z-score.
z = -3
The data item that corresponds to z = -3 is ___
(Type an integer or a decimal.)
Answer:
the data item that corresponds to z = -3 is 80.
Step-by-step explanation:
Which of the following statements assigns a random integer between 1 and 10, inclusive, to rn ?
A int rn = (int) (Math.random()) * 10;
B int rn = (int) (Math.random()) * 10 + 1;
C int rn = (int) (Math.random() * 10);
D int rn = (int) (Math.random() * 10) + 1;
E int rn = (int) (Math.random() + 1) * 10;
The correct statement that assigns a random integer between 1 and 10, inclusive, to rn is (D).
int rn = (int) (Math.random() * 10) + 1.
The method Math.random() generates a random number between 0 and 1, inclusive. If we multiply this number by 10, we will get a random number between 0 and 10, exclusive. If we then add 1 to this number, we will get a random number between 1 and 11, exclusive. If we then take the integer part of this number using the (int) cast, we will get a random integer between 1 and 10, inclusive. This is exactly what statement (D) does.
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Is the weight of a bike a function of how old it is?
The weight of an object is the amount of the gravitation pull of the Earth on the object. No, the weight of a bike is not a function of its age.
What i weight?The mass of an object is the quantity of matter it contains, while the weight is the amount of gravitational pull of the Earth on the object. Thus the greater the mass of an object is, the greater its weight. This implies that the weight of an object can be influenced by its value of mass.
The mass of an object can be determined or measured by the use of any of the weighing balances, while the weight of an object can be measured by the use of any of the spring balances. Therefore, the answer to the given question is NO. The weight of a bike is NOT a function of its age. The weight of the bike will depend on the number, and weight of its component parts.
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If f(x)=x^3-3x^2-18x+40f(x)=x 3 −3x 2 −18x+40 and f(-4)=0f(−4)=0, then find all of the zeros of f(x)f(x) algebraically.
By using algebra equation, the zeros of f(x)f(x) is ;
x = (-4 + 2i) and x = (-4 - 2i)
How to solve algebra equation ?Algebra is one of the numerous subfields of mathematics. The study of mathematical symbols and the rules for using them in formulas is commonly referred to as algebra, which runs across almost all of mathematics.Four methods can be used to solve one-step equations: addition, subtraction, multiplication, and division. If we add the same amount to both sides of an equation, both sides will remain equal.In algebra 1, we are introduced to the addition rule and the multiplication/division rule as two ways to solve problems. The equation addition rule states that the solution set of an equation can have the same amount added to both sides without changing.Given data :
This is a synthetic division shortcut. Write down the real root, then under a division symbol, the coefficients of the variables, 2, 18, 56, and 40. Drop down the 2 first, multiply by the root (-1) and add it to the next coefficient (18). 2*(-1) = -2, -2 + 18 = 16. Drop that one down. Next multiply 16 by the root, (-1) and add that to the next coefficient, 56 + (-16) = 40, drop down the 40, then lastly repeat this, multiply 40 by the root (-1) and add to the last coefficient 40 + (-40) = 0. If the remainder was not 0, then -1 would not have been a real root.
-1 | 2 18 56 40
......0 -2 -16 -40
--------------------
......2 16 40 0
Put these into another equation, (2x2 + 16x + 40)
Factoring out a 2 we get 2(x2 + 8x + 20)
The factors of 20 are 2*10 and 4*5. 2+10 = 12, 4+5 = 9, so we must use the quadratic equation to find our roots.
-8 ± √(64 - 4(20))/2 = -4 ± √(-16)/2 = -4 ± 4i/2 = -4 ± 2i
So the other two roots are x = (-4 + 2i) and x = (-4 - 2i)
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Which equation shows the quadratic formula used correctly to solve 7x² = 9+ x for x?
-1± √(1)²-4(7) (9)
2(7)
O
X=
X=
OX=
Ox=
1± √(-1)²-4(7)(9)
2(7)
-1± √(-1)² +4(7) (9)
2(7)
1± √(-1)² +4(7) (9)
2(7)
Answer: X= -1± √(-1)² - 4(7)(9)
2(7)
Step-by-step explanation: The correct equation for using the quadratic formula to solve 7x² = 9 + x for x is:
X= -1± √(-1)² - 4(7)(9)
2(7)
The quadratic formula is given by the equation X = -b ± √(b² - 4ac) / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, we have a = 7, b = 1, and c = 9, so plugging these values into the formula gives us the equation above.
The equation used to solve Quadratic Equation is -1 ± [√((-1)² - 4(7)(-9])/2(7)
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
we have the Quadratic Equation as:
7x² = 9+ x
7x² -x -9= 0
Using Discriminant method
x = -b ± √(b² -4ac)/2a
x = 1 ± √(1² - 4(7)(-9)/2(7)
x = 1 ± √(1 + 196)/14
Thus, the formula used 1 ± [√(1² - 4(7)(-9])/2(7)
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find the measure of m< YBA
The measure of an angle m ∠YBA=47°.
What is meant by an angle?In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.
Since,
ΔFBA=ΔYBA
The two triangles in the provided illustration are comparable.
So,
From the figure:
m ∠FBA=47°
So, m ∠YBA=47°
Therefore, the measure of angle m ∠YBA=47°
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Date Exchange Rate
October 8, 1982 267.38 Yen = 1 US dollar
June 30, 1995 84.90 Yen = 1 US dollar
a. Determine the cost, in US dollars, for a souvenir that cost 3,500 Yen
on October 8, 1982. Show your work in the provided space.
Using proportions, the value of 3500 Yen on October 8, 1982 is 13.1 USD
ProportionsProportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
On October 8, 1982;
267.38 Yen = 1US
The cost of 3500 Yen = ?
267.38 Yen = 1 USD
35000 Yen = x USD
Cross multiply both sides and solve for x
x * 267.38 = 3500 * 1
267.38x = 3500
Divide both sides by coefficient of x
267.38x / 267.38 = 3500 / 267.38
x = 13.1
The value of 3500 Yen is 13.1 USD
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Graph the image of the given triangle after the transformation that has the rule (x, y) → (x - 1, y + 5).
Select the Polygon tool. Click the points of the triangle vertices to create the triangle by connecting the sides.
A landscape architect designed a flower garden in the shape of a trapezoid.
The area of the garden is 13.92 square meters. A fence is planned around the perimeter of the garden. How many meters of fencing are needed?
By using area of trapezium, it can be calculated that-
Length of fencing needed in 15.88m
What is area of trapezium?
Area of trapezium is the total space taken by the trapezium.
If the length of parallel sides be a and b and distance between the parallel sides are d,
Area of trapezium = [tex]\frac{1}{2}\times(a + b) \times (d)[/tex]
Length of the parallel sides = [tex]b_1[/tex] m and 5.28 m
Length of non parallel sides = 3.3 m and 3.3 m
Distance between parallel sides = 3m
Area of trapezium = [tex]\frac{1}{2} \times (b_1 + 5.28) \times 3[/tex]
By the problem,
[tex]\frac{1}{2} \times (b_1 + 5.28) \times 3 = 13.92[/tex]
[tex]b_1 + 5.28 = 13.92 \times \frac{2}{3}\\b_1 + 5.28 = 9.28\\b_1 = 9.28 - 5.28\\b_1 = 4 \m[/tex]
Length of fencing needed = 4 + 5.28 + 3.3 + 3.3 = 15.88 m
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one and three fifths plus three and two thirds equals blank
Answer:
5 [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
1 [tex]\frac{3}{5}[/tex] = 8/5
3 [tex]\frac{2}{3}[/tex] = 11/3
In order to add fractions, the denominators, or the bottom numbers, have to be the same. To make them the same, find the common denominator (the lowest number that both the numbers can be divisible by)
8/5+ 11/3 the common denominator would be 15 so multiply the appropriate numbers to the denominators and the numerators (the top number)
24/15 + 55/15 = 79/15
Now simplify
79/15 = 5 [tex]\frac{4}{15}[/tex]
A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 35,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,200 miles with a standard deviation of 1200 miles. At α = 0.05, test the shipping firm's claim. Round the test statistic to the nearest thousandth.
Step 1) Write the null and alternative hypotheses.
Step 2) State a level of significance α. Determine the critical value and critical region.
Step 3) Compute the test statistic. Use classical approach or P-value approach.
Step4) Compare the critical value with test statistic or P-value with α.
Step5) State the conclusion.
Since H0 is not rejected so, the mean life of a contain brand of tire used by it's trucks is not less than 35,000 miles.
What is standard deviation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 35,000 miles.
To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,200 miles with a standard deviation of 1200 miles.
At α = 0.05, test the shipping firm's claim.
Under H0: μ 200 Vs H1: > 200 (Right tailed test)
n = 16, x bar = 205 , s = 14
Null Hypothesis; H0: μ = 35000 Vs H1: < 35000
(Mean life of brand of tire less than 35000 miles).
Under H0 test statistic is
t = (x bar - μ) / (s / √n) ≈ [tex]t_n_-_1[/tex]
Now, n = 18, x bar = 34,200, s = 12000
t = (34000 - 35000) / (1200 / √18) = -2.8284
t - critical value of α = 0.05 for left tailed at (18 - 1) df = -2.11
Therefore t calculated (= -2.8284) < -2.11
So, we do not reject H0.
Hence, since H0 is not rejected so, the mean life of a contain brand of tire used by it's trucks is not less than 35,000 miles.
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Help fast please !!!
Answer:
D.
Step-by-step explanation:
Thousandhts
Answer:
d. 7 thousandths
WHY?
0.007 places is a decimal representation of a number. In the decimal system, the value of a digit is determined by its position relative to the decimal point. In this case, the number 0.007 has three digits to the right of the decimal point, so it is said to have three decimal places. The value of each digit in this number is determined by its position: the first digit (0) is in the hundredths place, the second digit (0) is in the thousandths place, and the third digit (7) is in the ten-thousandths place.
Please help please and thank you
Answer:
11 inches
Step-by-step explanation:
If one inch represents 210 feet, then divide 2310 by 210 to get the number of inches in the scale drawing.
Answer:
11 inches
Step-by-step explanation:
2310/210 = 11
HELP FAST!!!!
INVESTMENTS Your aunt receives an inheritance of $20,000. She wants to
put some of the money into a savings account that earns 2% interest annually and
invest the rest in certificates of deposit (CDs) and bonds. A broker tells her that
CDs pay 5% interest annually and bonds pay 6% interest annually. She wants to
earn $1000 interest per year, and she wants to put twice as much money in CDs
as in bonds. How much should she put in each type of investment?
11.
Answer: She needs to invest 6,000 in bonds,6,000inbonds,12,000 in CDs and 2000 in the Savings account to earn a2000intheSavingsaccounttoearna1000 interest.
We follow these steps in order to arrive at the answer:
Let the amount invested in bonds be x
Since the amount to be invested in CDs is twice the investment in bonds, investment in CDs will 2x.
The amount to be invested in the savings bank will be 20000 - (x+2x)20000−(x+2x) or 20,000 - 3x20,000−3x
The interest earned on bonds will be 0.06x0.06x
The interest earned on CDs will be 2x*0.05 = 0.1x2x∗0.05=0.1x
The interest earned on the savings banks accounts will be (20,000-3x)*0.02 = 400-0.06x(20,000−3x)∗0.02=400−0.06x
The total expected interest of $1000 is the sum total of the interest earned from each of the three modes of investment.
Hence total interest is:
1000 = 0.06x + 0.1x+ 400 -0.06x1000=0.06x+0.1x+400−0.06x
Simplifying we get,
1000 -400 = 0.1x1000−400=0.1x
600 = 0.1x600=0.1x
\mathbf{x = 6,000}x=6,000
Since x represents investments in bonds, the investment in CDs will be \mathbf{2x = 2*6,000 = 12,000}2x=2∗6,000=12,000
Finally the investments in savings bank will be \mathbf{20000 - (12,000 + 6,000) = 20,000 - 18,000 = 2,000}20000−(12,000+6,000)=20,000−18,000=2,000
Write the equation of the line that has a slope of 1 and goes through the point (2, 3). Hint: Use y = mx+b
Answer:
y = x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
here m = 1 , then
y = x + c ← is the partial equation
to find c substitute (2, 3 ) into the partial equation
3 = 2 + c ⇒ c = 3 - 2 = 1
y = x + 1 ← equation of line
What is 7,899 to the nearest thousand
Answer: 8,000
Step-by-step explanation: So, to find how to round this to the nearest 1000, we need to look at the 3 digits being the 7. So, 899 is greater than 500, so we round up, so 7 + 1 is 8, and we change those 3 digits behind the zero to 0's, so we get 8,000. I hoped this helped.
Answer:
8000
7899 rounded to nearest thousand is 8000, because 7 is in thousand's place value, and the number after that is 8, which is more than 5, so 1 is added to 7, and it becomes 8. The rest of the numbers turn to 0.
so you get 8000.
hope it helps :)
NO LINKS!! Write an expression for the nth term of the geometric sequence. Then find the indicated term.
a1= 3, r = √(2), n = 10
a_n =
a_10=
Answer:
[tex]tn = {3 \times \sqrt{2} }^{n - 1} [/tex]
Step-by-step explanation:
since it is geometric sequence we will use the formula
[tex]tn = {ar}^{n - 1} [/tex]
n = 10
r = √2
a = 3
lets first see the result of the 10th term
[tex]t10 = {ar}^{10 - 1} [/tex]
[tex]t10 = {ar}^{9} [/tex]
[tex]t10 = {3 \times \sqrt{2} }^{9} [/tex]
t10 = 3 × 22.63
t10 = 67.89
approximately 68
t10 = 68
for the nth term
Tn = ar^n–1
[tex]tn = {3 \times (\sqrt{2} })^{n - 1} [/tex]
i hope this helps
Answer:
[tex]a_n=3\left(\sqrt{2}\right)^{n-1}[/tex]
[tex]a_{10}=48 \sqrt{2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
[tex]a = 3[/tex][tex]r = \sqrt{2}[/tex][tex]n=10[/tex]Substitute the given values of a and r into the formula to create an equation for the nth term:
[tex]a_n=3\left(\sqrt{2}\right)^{n-1}[/tex]
To find the 10th term, substitute n = 10 into the equation:
[tex]\implies a_{10}=3\left(\sqrt{2}\right)^{10-1}[/tex]
[tex]\implies a_{10}=3\left(\sqrt{2}\right)^{9}[/tex]
[tex]\implies a_{10}=3 \cdot 2^{\frac{9}{2}}[/tex]
[tex]\implies a_{10}=3 \cdot 2^{4+\frac{1}{2}}[/tex]
[tex]\implies a_{10}=3 \cdot 2^{4} \cdot 2^{\frac{1}{2}}[/tex]
[tex]\implies a_{10}=3 \cdot 16 \cdot \sqrt{2}[/tex]
[tex]\implies a_{10}=48 \sqrt{2}[/tex]