Answer:
[tex]f(x) = 4\times (3)^{x}[/tex].
Step-by-step explanation:
Exponential functions are in the form [tex]f(x) = a\, \left(b^{x}\right)[/tex], where [tex]a[/tex] and [tex]b[/tex] are constants with [tex]b > 0[/tex].
In this question, the function should satisfy that [tex]f(2) = 36[/tex] and [tex]f(3) = 108[/tex]. Hence, constants [tex]a[/tex] and [tex]b[/tex] should ensure that:
[tex]a \cdot b^2 = f(2) = 36[/tex], and
[tex]a \cdot b^3 = 108[/tex].
Rewrite the left-hand side of the second equation: [tex]a \cdot b^{3} = a \cdot b^2 \cdot b[/tex].
Substitute the first equation [tex]a \cdot b^{2} = 36[/tex] into the second:
[tex]a \cdot b^2 \cdot b = 108[/tex].
[tex]36\, b = 108[/tex].
[tex]\displaystyle b = \frac{108}{36} = 3[/tex].
Substitute [tex]b = 3[/tex] into either equation (for example, the first equation) and solve for [tex]a[/tex]:
[tex]a \cdot 3^2 = 36[/tex].
[tex]a = 4[/tex].
Hence, the exponential function [tex]f(x) = a\cdot b^{x} = 4 \times (3)^{x}[/tex] should satisfy the requirements of this question.
20x^2-12x-8
a. (10x+2) (2x+5)
b.(5x+2) (4x-4)
c. (5x-2) (4x+4)
d. (10x-2) (2x-5)
Answer:
B
Step-by-step explanation:
20x^2 - 12x - 8
4 ( 5x^2 - 3x - 2 )
5 * - 2 = - 10
Factors of - 10
1 , - 10
10, - 1
2, - 5
5, - 2
5x^2 - 5x + 2x - 2
5x (x - 1) 2 (x - 1)
4 (x - 1) (5x + 2)
(4x - 4) (5x + 2)
The difference between three times a number and 5 is 10.
Answer:
Equation: 3x-5=10
Answer: X=5
Step-by-step explanation:
3 times a number (represented as X) and 5 (means subtract by 5)
3x-5=10
Add 5 on both sides
3x=15
X=5
Answer:
3(5) - 5 = 10
15 - 5 = 10
10 = 10 x = 5
Step-by-step explanation:
Three times a number is 3x because you do not know the number.
Add five to both sides of the equation.
Divide both sides of the equation by 3 and the solution is x = 5
help please, thx <3
Answer: n=-42
Step-by-step explanation:
Take the given equation
-67 = n - 25
+25 +25
Add 25 to each side to cancel out the negative 25 on the right side
-67 + 25 = -42
n = -42
A marketing research consultant for a hotel chain hypothesizes that men and women differ in their color preference for guest rooms. The consultant shows pictures of rooms decorated with three different color scheme to each person in a random sample of 110 men and to each person in a random sample of 90 women. The consultant asks each person to choose his or her favorite color scheme. A chi-square test for homogeneity of proportions will be used to test the consultant’s hypothesis. Assuming that the conditions for inference are met, which of the following statements is true for the test?
A. The null hypothesis for the test is that the proportion of each gender who prefer each color scheme is
B. The sample size is too small to detect a significant difference in a chi-square test for homogeneity of proportions
C. The test is not valid because the sample sizes are not equal
D. The more that men and women differ in their color preferences, the larger the chi-square statistic will be
E. The test would also be appropriate if 90 married couples had been used for the two samples.
Answer:
D. The more that men and women differ in their color preferences, the larger the chi-square statistic will be.
Step-by-step explanation:
Hypothesis testing is a statistical technique which is used to identify the conclusion regarding whether to accept or reject the statistical statement. There is alternative hypothesis statement again which null hypothesis is tested.
Pleas help I will give brainliest also please show how you did it please
Answer:
for n ≤ 3
we are going to put a circle on the 3 and make it filled in then you are going to start an arrow starting from the 3 going to the left all the way to the -10.
Answer:
n ≥ -1 or n ≤ 3
Combined:
-1 ≤ n ≤ 3
Since the inequalities are ≤, it'll be a closed circle
The closed circle will start AT -1 and another closed circle will end at 3
Which is a feature of function g if g(x) = -f(x-4)
A) Y-Intercept at (0,-4)
B) X- intercept at (5,0)
C) vertical asymptote of x=-4
D) horizontal asymptote of Y=4
Answer:
B
Step-by-step explanation:
Plato
The x- intercept of g(x) is at (5,0), the correct option is B.
What is a Function?A function is a law that relates a dependent and an independent variable.
The function is g(x) = -f(x-4)
The x intercept is when y =0
The function in the graph f is 0 at x =1
g(x) = -f( 5-4) = -f(1) = 0
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Sandy knows that she needs $82,000 for a 15% down payment on a house she can afford. She found an investment that earns 3.25% interest
compounding monthly.
How much should she put in the account now, rounded to the nearest dollar, to ensure she has the down payment
amount in 5 years?
$12,034
$38,915
$69,717
$72,374
it is acceptable to divide by zero true or false
Answer:
flase.,......,........
Answer:
true
Step-by-step explanation:
so like for example you say 0÷50
your answer will remain 0
Melissa and Madeline love pepperoni pizza, but sometimes they are disappointed with the small number of pepperonis on their pizza. To investigate, they went to their favorite pizza restaurant at 10 random times during the week and ordered a large pepperoni pizza. Here are the numbers of pepperoni on each pizza.
47 36 25 37 46 36 49 32 32 34
Use the 4 step method to construct and interpret a 95% confidence interval for the true mean number of pepperonis on a large pizza at this restaurant.
Answer:
(31.919,42.881)
Step-by-step explanation:
Using the t-distribution, it is found that the 95% confidence interval for the true mean number of pepperonis on a large pizza at this restaurant is (31.92, 42.88). It means that we are 95% that the true mean number of pepperonis for all large pizzas at the restaurant is within this interval.
In this problem, we will find the standard deviation for the sample, hence the t-distribution will be used.
What is a t-distribution confidence interval?The confidence interval is given by:
[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.For this problem:
The sample size is n = 10.Using a calculator, we have that [tex]\overline{x} = 37.4, s = 7.66[/tex].The critical value, considering a 95% confidence interval with 10 - 1 = 9 df, is of t = 2.2622.The lower bound of the interval is:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 37.4 - 2.2622\frac{7.66}{\sqrt{10}} = 31.92[/tex]
The upper bound of the interval is:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 37.4 + 2.2622\frac{7.66}{\sqrt{10}} = 42.88[/tex]
The 95% confidence interval for the true mean number of pepperonis on a large pizza at this restaurant is (31.92, 42.88). It means that we are 95% that the true mean number of pepperonis for all large pizzas at the restaurant is within this interval.
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Use the quadratic formula to find the solution to the quadratic equation given below. x^2-3x+9/4 =0
Answer:
[tex] x = \dfrac{3}{2} [/tex]
Step-by-step explanation:
x^2-3x+9/4 =0
Multiply both sides by 4 to get rid of the fraction.
4x^2 - 12x + 9 = 0
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-(-12) \pm \sqrt{(-12)^2 - 4(4)(9)}}{2(4)} [/tex]
[tex] x = \dfrac{12 \pm \sqrt{144 - 144}}{8} [/tex]
[tex] x = \dfrac{12}{8} [/tex]
[tex] x = \dfrac{3}{2} [/tex]
Find the missing value(s) in this ratio table. Pens: 3 6 ? Pencils: 4 ? 12
Pen is 3 x 2 = 6
Pencils s 4 x 3 = 12
Natasha conducted a survey to determine how many of the 215 workers in her office building use public transportation to get to work. She surveyed 30 randomly selected workers who entered the office cafeteria throughout the day. Of the 30 workers surveyed, 9 used public transportation to get to work. Which change to Natasha's survey process would make the data more reliable? A. Randomly select the sample in the lobby of the building so workers who do not enter the cafeteria can be included. B. Have workers complete a written survey so there is a written record of the responses. C. Ask a randomly selected sample of people who use public transportation whether their office is in the building. D. Use a different sample size so the predicted number of workers who use public transportation is a whole number.
Answer:
A. Randomly select the sample in the lobby of the building so workers who do not enter the cafeteria can be included.
Step-by-step explanation:
Randomly select the sample in the lobby of the building so workers who do not enter the cafeteria can be included.
We have given that,
Natasha conducted a survey to determine how many of the 215 workers in her office building use public transportation to get to work. She surveyed 30 randomly selected workers who entered the office cafeteria throughout the day. Of the 30 workers surveyed, 9 used public transportation to get to work.
We have to determine that,
a change to Natasha's survey process would make the data more reliable.
What is random selection?
Random sampling, or probability sampling, is a sampling method that allows for the randomization of sample selection each sample has the same probability as other samples to be selected to serve as a representation of an entire population.
Randomly select the sample in the lobby of the building
So workers who do not enter the cafeteria can be included.
Therefore the correct option is A.
Thus, Randomly select the sample in the lobby of the building so workers who do not enter the cafeteria can be included.
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I’ll give points and brainalist for correct answer
Answer:
A. 2
Step-by-step explanation:
Circumference of a circle = 2πr
if π = 3.14
and C = 6.28
6.28 = 2(3.14)r
r= 1
d= 2r
d= 2 * 1
d= 2
In a particular library, 18% of the books are children's books, 53% of the books are adult fiction, and the rest are adult nonfiction. You select 3 books at random; what is the probability That none of them are children's books?
Answer:
3321 / 12500
Step-by-step explanation:
P (not child, not child, not child) = 82/100 × 81/100 × 80/100
I need help quick just the first one
Answer:9& 5
Step-by-step explanation:
Emilio spent $21 at the state
fair. He paid $3 for admission and bought
12 tickets for rides. Solve the equation
12t +3= 21 to find the cost of each
ticket
Answer:
t = $1.5Steps:
12t+3 = 21
12t = 21-3
12t = 18
t = 18/12
t = 3/2
t = $1.5Find the area of the shape shown below.
Answer:
6
Step-by-step explanation:
Area of sq:
A = bh
A = (2)(2)
A = 4
Area of triangle:
A = 1/2bh
A = 1/2(2)(2)
A = 2
Combined:
4 + 2 = 6
Find the surface area of a basketball with a diameter of 10 in.
400π in²
10π in²
100π in²
25π in²
Answer:
100 pie
Step-by-step explanation:
Find the surface area of a basketball with a diameter of 10 in.
100π in²
10π in²
400π in²
25π in²
The surface area of the basketball is 100π square inches.
The correct option is C.
What is the surface area of a sphere?The area of the outer surface of a sphere is the surface area of a sphere.
And its formula:
The surface area of the sphere is 4πr².
Where r is the radius of the sphere.
Given:
The shape of the basketball is spherical.
The diameter of the basketball is 10 inches.
So, the radius of the basketball = 10/2 = 5 inches.
The surface area of the basketball,
= the surface area of the sphere.
= 4πr²
= 4π(5)²
= 2π25
= 4 x 25π
= 100π square inches.
Therefore, the surface area is 100π square inches.
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How many solutions will the system of linear equations have: y = x + 6 and 3x - 3y = -18
Answer:
If i'm not mistaken, infinite because its linear which is a straight line that goes on forever
Step-by-step explanation:
lll give points and brainalist for correct answer / explanation
Answer:
D
Step-by-step explanation:
A. false; the diameter of a circle is double the radius
B. false; the diameter of a circle is double the radius
C. false; the diameter of a circle is double the radius
D. true! The diameter is double the radius
What is the explicit formula for the geometric sequence 15, 3, 0.6,
0.12, ...?
Answer:
A
Step-by-step explanation:
first num is 15
ratio is 0.2
formula is a.r^n-1
Use the distributive property to write an equivalent expression. 4(2x+3)
Answer:
20x
Step-by-step explanation:
4(2x+3)
4(5x)
4x5x
20x
buna seara ce faceti eu sunt un om
Answer:
5
Step-by-step explanation:
Answer:
Sunt și bărbat, ești foarte înfiorător
Step-by-step explanation:
What is the Equation of the line
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 1) and (x₂, y₂ ) = (4, - 3)
m = [tex]\frac{-3-1}{4+4}[/tex] = [tex]\frac{-4}{8}[/tex] = - [tex]\frac{1}{2}[/tex]
The line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = - [tex]\frac{1}{2}[/tex] x - 1 ← equation of line
what is the answer for this math problem ^
Answer: 12
Step-by-step explanation:
A school band performed a concert on four different days. The band sold tickets and snacks each day of the concert for a fundraiser. The first table shows the numbers of tickets sold and the amounts of money collected from ticket sales. The second table shows the numbers of snacks sold and the amounts of money collected from snack sales. If each snack costs the same price, what is the price per snack?
Answer:
$1.25
Step-by-step explanation:
There is a lot of unnecessary extra information we can ignore here. Simply divide the amount collected on any given day by the number of snacks sold.
53.75 / 43 = $1.25
Double check via another day:
45 / 36 = $1.25 ~ yup!
The price per snack is $1.25.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
From the table,
We see that,
43 snacks = $53.75
This means,
1 snack = 53.75/43 = 1.25
Similarly,
36 snacks = 45
1 snack = 45/36 = 1.25
Thus,
The price per snack is $1.25.
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need help with this ‼️
Remember to do the opposite operation of what you see in the equation.
4x=16
x=16/4=4 is the answer if u need any explanation please comment
hope it helps
Answer:
x=4
Step-by-step explanation:
4x = 16
Divide each side by 4:
x=4
(WORTH 25 POINTS and il give brainliest to the first person to answer) Miguel is building a doghouse he cuts one sheet of wood to make the front wall he also cuts out a door that is 2 ft by 2 ft the dimensions in feet are shown in the diagram. miguel needs to paint the wood. what is the area he needs to paint? 1. what is the area of the rectangular price of wood before the square is cut out? include units with your answer.
Answer:
umm 4 ft
Step-by-step explanation:
Answer:
12 ft sq.
Step-by-step explanation:
help please
find the surface area of the following prism
Answer: 163
Step-by-step explanation: