There are 82 people you should survey if you want to know, at a 98% confidence level, that the sample mean SAT score is within 50 points of the true mean SAT score.
We have,
a college board sample estimated the standard deviation of 2016 SAT scores to be 194 points.
We used the formula,
= x ± Z (α/2) × σ/√n
Here, α = 1 - 98% = 0.02
Z (α/2) = Z (0.02/2) = 2.326
Hence, We get;
Z (α/2) × σ/√n = 50
2.326 x 194 /√n = 50
√n = 2.326 x 194 / 50
n = 82
Therefore, There are 82 people you should survey if you want to know, at a 98% confidence level, that the sample mean SAT score is within 50 points of the true mean SAT score.
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not rushing anyone but if someone wants to help rq thatd be great
a. The solution to the equation f - 13 = 51 is f = 64.
b. The solution to the equation x/10 = 4 is x = 40.
a. f - 13 = 51
Step 1: Add 13 to both sides to isolate f.
f - 13 + 13 = 51 + 13
Step 2: Simplify.
f = 64
Step 3: Check the answer by substituting f = 64 back into the original equation.
64 - 13 = 51
51 = 51
The answer checks out.
b. (x/10) = 4
Step 1: Multiply both sides by 10 to isolate x.
10(x/10) = 4(10)
Step 2: Simplify.
x = 40
Step 3: Check the answer by substituting x = 40 back into the original equation.
40/10 = 4
4 = 4
The answer checks out.
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[tex]\frac{1}{4} x \frac{25}{25} =[/tex]
The value of the product is 1/4
How to determine the productTo determine the value of the product, we need to take note that fractions are described as the part of a whole number, element, or variable.
In mathematics, there are different types of fractions, namely;
Simple fractionsComplex fractionsImproper fractionsProper fractionsMixed fractionsFrom the information given, we have that;
1/4 × 25/25
Now, multiply the numerators
25/4(25)
Multiply the denominators
25/100
Divide the values
1/4
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in an isosceles triangle, one base angle measures 60 degrees. what is the measure of the third angle?
Therefore, the measure of the third angle in this isosceles triangle is 60 degrees.
By definition, an isosceles triangle has two sides of equal length, and in this case, two congruent base angles. The third angle, which is not part of the base, is opposite the third side of the triangle.
Since the sum of the measures of the angles in any triangle is always 180 degrees, we can use this fact to find the measure of the third angle in the isosceles triangle. We know that one of the base angles measures 60 degrees, and since the other base angle is also congruent, it also measures 60 degrees. Therefore, the total measure of the base angles is 60 degrees + 60 degrees = 120 degrees.
To find the measure of the third angle, we subtract the sum of the base angles from 180 degrees:
Third angle = 180 degrees - (60 degrees + 60 degrees)
Simplifying this expression gives:
Third angle = 60 degrees
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Js need a simple answer
Answer:
the tenth letter of the alphabet.
Step-by-step explanation:
Js is just the plural version of J.
Answer:a simple answer
Step-by-step explanation:the question asks: "Js need a simple answer"
So what they need is "a simple answer"!
The surface area of a cube is 2646 cm2 what is the length of each edge
Answer:
The length of each edge of the cube is 21 cm.
Step-by-step explanation:
The surface area of a cube is given by the formula:
SA = 6s^2
where SA is the surface area and s is the length of each edge.
We can rearrange this formula to solve for s:
s = sqrt(SA/6)
Substituting the given value of SA = 2646 cm^2, we get:
s = sqrt(2646/6)
s = sqrt(441)
s = 21
Therefore, the length of each edge of the cube is 21 cm.
In a Cartesian coordinate system for a three-dimensional space.
Sphere (S) is represented by equation: [tex](x-1)^2+(y+2)^2+(z-3)^2=25[/tex].
Plane (P) is represented by equation: [tex]x+2y-2z+1=0[/tex].
Line (d) is parallel to (P), passes through the origin and passes through (S) at two separate points A & B. Find the maximum length of AB.
In a Cartesian coordinate system for a three-dimensional space, let the sphere S be represented by the equation:
(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2
where (a, b, c) are the coordinates of the center of the sphere, and r is the radius.
Let the plane P be represented by the equation:
Ax + By + Cz + D = 0
where (A, B, C) is the normal vector to the plane.
Since the line d is parallel to P and passes through the origin, it can be represented by the equation:
lx + my + nz = 0
where (l, m, n) is a vector parallel to the plane P.
To find the intersection points of the sphere S and the line d, we can substitute the equation of the line into the equation of the sphere, which gives us a quadratic equation in t:
(lt - a)^2 + (mt - b)^2 + (nt - c)^2 = r^2
Expanding this equation and collecting terms, we get:
(l^2 + m^2 + n^2) t^2 - 2(al + bm + cn) t + (a^2 + b^2 + c^2 - r^2) = 0
Since the line d passes through the origin, we have:
l(0 - a) + m(0 - b) + n(0 - c) = 0
which simplifies to:
al + bm + cn = 0
Therefore, the quadratic equation reduces to:
(l^2 + m^2 + n^2) t^2 + (a^2 + b^2 + c^2 - r^2) = 0
This equation has two solutions for t, which correspond to the two intersection points of the line d and the sphere S:
t1 = -(a^2 + b^2 + c^2 - r^2) / (l^2 + m^2 + n^2)
t2 = -t1
The coordinates of the intersection points can be obtained by substituting these values of t into the equation of the line d:
A = lt1, B = mt1, C = nt1
and
D = lt2, E = mt2, F = nt2
To find the distance between A and B, we can use the distance formula:
AB = sqrt((A - D)^2 + (B - E)^2 + (C - F)^2)
To maximize this distance, we can differentiate the distance formula with respect to t1 and set the derivative equal to zero:
d/dt1 (AB)^2 = 2(A - D)l + 2(B - E)m + 2(C - F)n = 0
This equation represents the condition that the direction vector (A - D, B - E, C - F) is orthogonal to the line d. Therefore, the vector (A - D, B - E, C - F) is parallel to the normal vector (l, m, n) of the plane P.
Using this condition, we can find the values of t1 and t2 that correspond to the maximum distance AB. Then we can substitute these values into the distance formula to find the maximum length of AB.
Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.
Checking for approximate normality in the population is essential for constructing a valid confidence interval, particularly when dealing with small sample sizes. This ensures the accuracy and reliability of the interval in estimating the true population parameter.
It's important to check whether the population is approximately normal before constructing a confidence interval because the accuracy and validity of the interval depend on the underlying distribution of the population. Here's a step-by-step explanation:
1. A confidence interval is a range of values within which the true population parameter (e.g., mean or proportion) is likely to fall, with a certain level of confidence (e.g., 95% or 99%).
2. The process of constructing a confidence interval relies on the Central Limit Theorem, which states that, for large sample sizes, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.
3. However, for small sample sizes, the distribution of the population needs to be approximately normal in order to obtain an accurate confidence interval. This is because the normality assumption is crucial for the proper interpretation of the interval.
4. If the population is not approximately normal, the confidence interval may not provide a reliable estimate of the true population parameter, leading to incorrect conclusions and potentially invalid results.
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In ΔRST, r = 94 inches, s = 78 inches and ∠T=49°. Find the area of ΔRST, to the nearest square inch.
The area of ΔRST is 2767 square inches.
We have,
r = 94 inches, s = 78 inches and ∠T=49
We will use the formula
Area= 1/2 a b sin C
So, area of ΔRST
= 1/2 r s sin <T
= 1/2 (94) (78) sin (49)
= 3666 sin(49)
= 2766.7653
= 2767 square inches
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What type of test is more appropriate when you want to compare an outcome between the same two people at different time points?
The appropriate test to use in this situation is a paired t-test. This test is used to determine if there is a significant difference between two related samples, in this case, the same individuals at two different time points.
In this scenario, a paired t-test is the most suitable test because it is used to analyze paired data, where the same individuals are measured or tested at two different time points. The paired t-test takes into account the correlation between the two measurements within each individual and compares the mean difference between the paired observations to determine if there is a statistically significant change over time.
It is commonly used in longitudinal studies, clinical trials with repeated measures, or before-and-after intervention studies, where the focus is on comparing the same individuals' outcomes over time rather than comparing different groups or populations.
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1
If y varies inversely as x, and y = 2/5 when x = 2, find y when x = 1.
Find the constant of variation for the relation and use it to write an equation for the statement. The solve the equation
Answer:
[tex] \frac{1}{5} [/tex]
Step-by-step explanation:
[tex] \frac{2}{5} = y \: \\ x \ = 2 \\ \frac{ \frac{2}{5} }{2} = \frac{2}{2} \: \\ \frac{1}{5} = y \: when \: \: 1= x[/tex]
Help me with this math problem..... URGENT!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The answer is D
Step-by-step explanation:
You just find the cubed root of each value (ex. the cubed root of 27 is 3)
To check your answer, give x y and z value (I did x=2 y=3 and z=4)
Then solve both equations (your answer and the original equation)
If it matches you are right
an art supply company's sales this year were 180% of what they were 5 years ago. if sales 5 years ago were $25,000. what were this years sales?
If the sales 5 years ago were $25,000, then we can calculate this year's sales as follows:
Calculate the percentage increase from 5 years ago to this year:
Percentage increase = 180% - 100% = 80%
Calculate the amount of increase in sales:
Amount of increase = Percentage increase x Sales 5 years ago
Amount of increase = 0.8 x $25,000 = $20,000
Add the amount of increase to the sales 5 years ago to find this year's sales:
This year's sales = Sales 5 years ago + Amount of increase
This year's sales = $25,000 + $20,000 = $45,000
Therefore, this year's sales for the art supply company were $45,000.
I NEED HELP ON THIS ASAP!!
a) The function that has a greater b value is given as follows: Function B.
b) Both functions have an horizontal asymptote at y = 0.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.For Function B, we have that when x increases by one, y is multiplied by a value greater than 3, as:
When x = 0, y = 2.When x = 1, y > 6.Hence function B has a greater b-value.
Both functions have an horizontal asymptote at y = 0, as we can see from the graph of function B, as well as from the fact that there is no adding/subtracting term in function A.
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What are the domain and range of f(x) = 2(3x)? domain: (negative infinity, infinity); range: (0, infinity) domain: (negative infinity, infinity); range: (2, infinity) domain: (0, infinity); range: (negative infinity, infinity) domain: (2, infinity); range: (negative infinity, infinity)
The given function is f(x) = 2(3x) = 6x.
The domain of the function is all real numbers since there are no restrictions on the input x. Therefore, the correct answer is:
Domain: (-∞, ∞)
To find the range, we can consider the fact that the function is a linear function with a positive slope of 6. This means that the output values increase as the input values increase.
The lowest possible output value occurs when x = 0, which gives f(0) = 0. As x increases, the output values increase without bound. Therefore, the range of the function is:
Range: (0, ∞)
So, the correct answer is:
Domain: (-∞, ∞)
Range: (0, ∞)
√361 is rational/ irrational
Answer:
Step-by-step explanation:
irrational.
[tex]\sqrt{x} 361 = 19\\and 19 is irrational[/tex]
Answer: The answer is irrational. In order to find this out if you have a calculator you can put this number into it and it will tell you if it's rational or irrational. Calculator type TI-30Xa.
Step-by-step explanation: Please give Brainlist.
Hope this helps!!!!
I can answer more questions if you wish.
Let A and B be two events. Suppose that P (A)=0.45 and P(B)=0.16.
(a) Find ,P(A or B) given that and are independent.
(b) Find ,P(A or B) given that and are mutually exclusive.
Answer: The answer is 0.16. i hope I helped you god bless you.
Step-by-step explanation:
Find the area of the figure.
Answer:1,703,520
Step-by-step explanation:
26 x 14 x 26 x 180
In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.
The graph represents which system of inequalities?
A. y ≤ −3x − 1
y ≤ −x − 4
B. y > −3x + 1
y ≤ −x − 4
C. y < 3x − 1
y ≤ −x + 4
D. y ≤ 3x − 1
y ≥ −x + 4
The equations of the line will be x + y ≤ 4 and 3x - y > 1. Then the correct option is C.
Given that:
Intercept of line g(x), a = 4 and b = 4
Intercept of dashed line f(x), a = 1/3 and b = -1
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The equation of line g(x) is calculated as,
x/4 + y/4 ≤ 1
x + y ≤ 4
The equation of dashed line f(x) is calculated as,
x/(1/3) + y/(-1) > 1
3x - y > 1
The equations of the line will be x + y ≤ 4 and 3x - y > 1. Then the correct option is C.
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Consider a set of six classes, each meeting regularly once a week on a particular day of the week. Choose the statement that best explains why there must be at least two classes that meet on the same day. assuming that no classes are held on weekends: a. The pigeonhole principle shows that in any set of six classes there must be more than two classes that meet on the same day because there are only five weekdays for each class to meet on. b. The pigeonhole principle shows that in any set of six classes there must be at least two classes that meet on the same day because there are only five weekdays for each class to c. The pigeonhole principle shows that in any set of six classes there must be exactly two classes that meet on the same day because there are only five weekdays for each class to d. The pigeonhole principle shows that in any set of six classes there must be at least two classes that meet on the same day because there are more than two classes in total meet on meet on.
The pigeonhole principle shows that in any set of six classes, there must be at least two classes that meet on the same day because there are only five weekdays for each class to meet on.
This principle states that if there are more items than the number of spaces available to place them in, at least two items must occupy the same space. In this case, there are six classes and only five weekdays available for each class to meet on. Therefore, at least two classes must meet on the same day.
Correct answer: b. The pigeonhole principle shows that in any set of six classes, there must be at least two classes that meet on the same day because there are only five weekdays for each class to meet on.
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which rectangle has side lengths of 5 units and 4 units?
A) A(3,3), B(3,6), C(8,6), D(8,3)
B) A(3,3), B(3,7), C(8,7), D(8,3)
C) A(3,3), B(3,7), C(7,7), D(7,3)
D) A(3,3), B(3,8), C(8,8), D(8,3)
The rectangle that has side lengths of 5 units and 4 units is C) A(3,3), B(3,7), C(7,7), D(7,3).
Point C at (7,7), means the width is 4 units (7-3) and the height is 5 units (7-2), so this is the correct rectangle.
What is a rectangle?A rectangle is a shape with four right angles (that is four angles of 90 degrees) and the opposite sides are parallel and congruent.
The two sides of a rectangle are parallel and they meet at the four corners or vertices.
For a rectangle, the opposite sides are of the same length and are parallel to each other.
Therefore, C. A(3,3), B(3,7), C(7,7), D(7,3) is the rectangle that has side lengths of 5 units and 4 units.
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You measure 47 backpacks' weights, and find they have a mean weight of 66 ounces.
Assume the population standard deviation is 8.2 ounces. Based on this, what is the maximal margin of error associated with a 99% confidence interval for the true population mean backpack weight.
Give your answer as a decimal, to two places
The maximal margin of error associated with a 99% confidence interval for the true population mean backpack weight is 2.73 ounces (rounded to two decimal places).
We can use the formula for the margin of error in a confidence interval:
margin of error = z ×(σ / √n)
where:
z is the z-score corresponding to the desired level of confidence (99% in this case), σ is the standard deviation, n is the sample size
For a 99% confidence level, the z-score is approximately 2.576.
Substituting the given values into the formula, we get:
margin of error = 2.576 × (8.2 / √47
margin of error = 2.73
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If 6 × ∎ = 420, what number does ∎ represent?
if equation 6 × ∎ = 420 then the value of ∎ is 70.
Given that 6 × ∎ = 420
We have to find the value ∎
Let us consider ∎ as x
6×x=420
To find the value of x we have to divide both sides by 6
x=420/6
x=70
Hence, if 6 × ∎ = 420 then the value of ∎ is 70.
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A piece of paper is 8.5in by 11n. Imagine repeatedly folding the paper in half. What happens to the area of paper after each fold? Write an exponential function to find the area of paper after each fold.
Answer:
A = (93.5/2^(2n)) After each fold, the area of the paper is halved.
Step-by-step explanation:
When the paper is folded in half, the length and width of the paper are each halved, which means that the area of the paper is also halved. If we continue to fold the paper in half, the area will continue to be halved with each fold.
To write an exponential function to find the area of the paper after each fold, we can use the formula for the area of a rectangle, A = lw, where A is the area, l is the length, and w is the width. Since the length and width are both halved with each fold, we can represent this as:
A = (8.5/2^n)(11/2^n)
where n is the number of folds. To simplify this, we can combine the terms under the same exponent and get:
Answer:
A(n) = 93.5 / 2^(2n-1)
Step-by-step explanation:
Each time the paper is folded in half, its length and width are halved. Therefore, the area of the paper is also halved after each fold.
Let A₀ be the initial area of the paper, which is 8.5 inches by 11 inches, or 93.5 square inches (rounded to one decimal place). After the first fold, the area becomes:
A₁ = (8.5/2) x 11 = 46.75 square inches
After the second fold, the area becomes:
A₂ = (8.5/2) x (11/2) = 23.375 square inches
And so on.
Therefore, the exponential function to find the area of the paper after each fold is:
A(n) = 93.5 / 2^(2n-1)
Geometry: Transformations
How many lines of symmetry does the following figure have?
A) 14
B) 8
C) 2
D) 4
The life in hours of a 75-watt light bulb is known to be normally distributed with σ=25hours. A random sample of 20 bulbs has a mean life of ¯x=1014 hours.Construct a 95% two sided confidence interval on the mean life.Construct a 95% lower confidence bound on the mean life.
For a 95% lower confidence bound, we only need the lower limit. The 95% lower confidence bound on the mean life of a 75-watt light bulb is approximately 1003.045 hours.
To construct a 95% two-sided confidence interval on the mean life, we can use the formula:
CI = x ± tα/2 * (σ/√n)
where x is the sample mean (1014 hours), σ is the population standard deviation (25 hours), n is the sample size (20), and tα/2 is the critical value from the t-distribution with (n-1) degrees of freedom at a significance level of α/2 = 0.025 (since we want a 95% confidence interval).
Using a t-table or calculator, we can find that t0.025,19 = 2.093. Substituting these values into the formula, we get:
CI = 1014 ± 2.093 * (25/√20) = (970.5, 1057.5)
Therefore, we are 95% confident that the true mean life of the 75-watt light bulb is between 970.5 hours and 1057.5 hours.
To construct a 95% lower confidence bound on the mean life, we can use the formula:
LB = x - tα * (σ/√n)
where LB is the lower bound, x is the sample mean, σ is the population standard deviation, n is the sample size, and tα is the critical value from the t-distribution with (n-1) degrees of freedom at a significance level of α = 0.05 (since we want a one-sided confidence bound).
Using the same values as before, we can find that t0.05,19 = 1.734. Substituting these values into the formula, we get:
LB = 1014 - 1.734 * (25/√20) = 991.2
Therefore, we are 95% confident that the true mean life of the 75-watt light bulb is at least 991.2 hours.
Step 1: Identify the given information
- Sample mean (x) = 1014 hours
- Sample size (n) = 20 bulbs
- Population standard deviation (σ) = 25 hours
- Confidence level = 95%
Step 2: Calculate the standard error (SE)
SE = σ / √n = 25 / √20 = 5.590
Step 3: Find the critical value (z) for the 95% confidence level (two-sided)
For a 95% confidence interval, the z-value is 1.96.
Step 4: Calculate the margin of error (ME)
ME = z * SE = 1.96 * 5.590 = 10.955
Step 5: Construct the 95% confidence interval
Lower limit = x - ME = 1014 - 10.955 = 1003.045
Upper limit = x + ME = 1014 + 10.955 = 1024.955
The 95% two-sided confidence interval on the mean life of a 75-watt light bulb is approximately (1003.045 hours, 1024.955 hours).
Step 6: Construct the 95% lower confidence bound
For a 95% lower confidence bound, we only need the lower limit.
The 95% lower confidence bound on the mean life of a 75-watt light bulb is approximately 1003.045 hours.
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I need to find the ordered pairs
The total possible combination of ordered pairs from the element of the given set is 9
What are the ordered pairsTo find the ordered pairs of the equation, we simply have to find the total possible combinations from the element of the set.
The element of set given is x ∈ {-1, 0, 1}
The possible combinations of x ∈ {-1, 0, 1} are;
(-1, -1)
(-1, 0)
(0, -1)
(1, 1)
(-1, 1)
(1, -1)
(0, 1)
(1, 0)
(0, 0)
We have 9 possible ordered pairs
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An industrial pipeline welder is comparing pension plans for two different job offers
First offer: $66,421 average annual wage, 1.9% per year of service, with a monthly pension payment of $3,155 after 30 years of service
Second offer $87,000 average annual wage, 1.5% per year of service
The welder plans to work for the same amount of time at each company. What is the difference in monthly pension payments?
O The second offer pays $170.50 more per month
O The first offer pays $170.50 more per month
O The second offer pays $107.50 more per month
O The first offer pays $107.50 more per month
The difference in monthly pension payments is that the second offer pays $170.50 more per month.
What is the difference in monthly pension payments?For the first offer:
The annual pension payment will be:
= Average annual wage x (1.9% per year of service) x 30 years
= $66,421 x (0.019) x 30
= $37859.97
Monthly pension payment:
= Annual pension payment / 12
= $37859.97 / 12
= $3,154.99
For the second offer:
The annual pension payment will be:
= Average annual wage x (1.5% per year of service) x 30 years
= $87,000 x (0.015) x 30
= $39150
The monthly pension payment will be:
= Annual pension payment / 12
= $39150 / 12
= $3262.5
The difference in monthly pension payments between the two offers is:
= $3262.50 - $3,155
= $107.50.
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HELP!!!!
Please help!!!
The lengths of three metal rods, A, B and C, are such that length of A : length of B = 3 : 2 and
length of A : length of C = 2 : 5
The difference in length between the longest rod and the shortest rod is 55 cm. Find the total length of the three rod in metres.
The lengths of rods A, B and C are respectively;
30 cm, 10 cm and 75 cm
How to solve ratio problems?We are given that;
Ratio of length of Rod A to length of Rod B is; 3:2
Ratio of length of Rod A to length of rod C is 2:5
Thus;
2/3 Length of Rod A = the length of Rod B
5/2 Length of Rod A = the length of Rod C
If length of Rod A = x, then we can say that;
5x/2 is length of Rod C
⅔x is the lenggh of Rod B
Difference between longest and shortest is 55. Thus;
(5/2)x - (2/3)x = 55
Multiply through by 6 to get;
15x - 4x = 330
11x = 330
x = 330/11
x = 30 cm
Length of Rod B = (2/3) * 30
= 10 cm
Length of Rod C = (5/2) * 30
= 75 cm
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Using a calculator, work out the value of (8.8 × 10-4) x (7.4 x 1011) Give your answer in standard form
The required value of (8.8 × 10⁻⁴) × (7.4 x 10¹¹) in standard form is 6.512 × 10⁸.
The expression is given as follows:
(8.8 × 10⁻⁴) × (7.4 x 10¹¹)
When multiplying numbers in scientific notation, we can multiply the coefficients and add the exponents of 10.
(8.8 × 10⁻⁴) × (7.4 x 10¹¹)
= (8.8 × 7.4) × 10⁽⁻⁴⁺¹¹⁾
= 65.12 × 10⁷
To convert to standard form, we can write 65.12 as 6.512 × 10¹:
= 6.512 × 10¹ × 10⁷
= 6.512 × 10⁸
Therefore, the value of (8.8 × 10⁻⁴) × (7.4 x 10¹¹) in standard form is 6.512 × 10⁸.
Learn more about the standard form here:
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Charlie has 2 gallons of milk. He uses 2 pints a day. How long can he use the milk?
