Will Mark brainliest.

The exponential function in the form y= ab^x is y = 16(2)^7

From the question, we have the following parameters that can be used in our computation:

Function that goes through points (0,16) and (7,2048)

An exponential function is represented as

y = ab^x

Where

a = y when x = 0

This means that

a = 16

So, we have

y = 16b^x

Using the other point, we have

16b^7 = 2048

Divide

b^7 = 128

So, we have

b = 7

So, the function is y = 16(2)^7

Read more about exponential function at

https://brainly.com/question/2456547

#SPJ1

The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

To learn more on angle click:

brainly.com/question/28451077

#SPJ1

complete question:

Find the value of each variable

1. Adjusted balance after the first payment: $27,225.

2. Adjusted balance after the second payment: $10,857.

3. Balance at maturity: $10,911.

1. Adjusted balance after the first payment:

Interest accrued in the first 75 days:

= $39,600 x 6% x 75/360

= $495

The adjusted balance after the first payment:

= $39,600 - $11,880 - $495

= $27,225

2. Adjusted balance after the second payment:

Interest accrued in the first 80 days:

= $39,600 x 6% x 80/360

= $528

Adjusted balance after the second payment:

= $27,225 - $15,840 - $528

= $10,857

3. Balance at maturity:

Interest accrued in the remaining 30 days:

= $10,857 x 6% x 30/360

= $54

Balance at maturity:

= $10,857 + $54

= $10,911

Read more about balance

brainly.com/question/1403056

#SPJ1

The total surface area of the given triangular prism is: 72.5 in²

To get the surface area of this prism, what we will do is to find the area of each of the surfaces and add up to get the total surface area.

The formula for the area of a triangle is:

Area = ¹/₂ * b * h'

where:

b is base length

h is height

Total Surface Area = (¹/₂(5 * 5)) + 3(¹/₂*5*8)

Total Surface Area = (25/2) + 60

Total Surface Area = 72.5 in²

Read more about surface area of prism at: https://brainly.com/question/1297098

#SPJ1

The incorrect statement is the reflection is over x-axis.

Given that an image has been reflected to form another image, we need to find the incorrect statement from the given options,

A reflection is known as a flip.

A reflection is a mirror image of the shape.

An image will reflect through a line, known as the line of reflection.

A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

So, here the image is reflected over y-axis so the rule (x, y) → (-x, y) can be followed,

Also, the orientation of the image is preserved.

Since, the transformation is reflection, so the image and pre-images are congruent.

Hence, the incorrect statement is the reflection is over x-axis.

Learn more about transformations, click;

https://brainly.com/question/11709244

#SPJ1

The incorrect statement is the reflection is over x-axis.

Given that,

an image has been reflected to form another image, we need to find the incorrect statement from the given options,

So, here the image is reflected over y-axis so the rule (x, y) → (-x, y) can be followed,

Also, the orientation of the image is preserved.

Since, the transformation is reflection, so the image and pre-images are congruent.

Hence, the incorrect statement is the reflection is over x-axis.

Learn more about transformations, click;

brainly.com/question/11709244

#SPJ1

The probability of event B is P(B) = 1/2

From the Venn diagram, we can observe that there are two events A and event B

n(A ∪ B) = 6 + 6 + 20

n(A ∪ B) = 32

And n(A ∩ B) = 6

The sample space would be,

n(S) = 6 + 6 + 20 + 20

n(S) = 12 + 40

n(S) = 52

And the number of outcomes for event B would be,

n(B) = 20 + 6

n(B) = 26

Using the definition of probability,

P(B) = n(B)/n(S)

P(B) = 26/52

P(B) = 1/2

This is the required probability.

Learn more about the probability here:

https://brainly.com/question/15124899

#SPJ1

Answer:

0.50

Step-by-step explanation:

Volume is found by multiplying length x width x height

The value of the k is; 1/12

The proportion is given by the expression;

y = kxz

Given the values;

y=6 when x=4 and z=12

To find the constant, k;

6 = k*4*12

6= 48k

k = 4/48

k = 1/12

More can be learned about proportions at;

brainly.com/question/24372153

#SPJ1

The equation of the ellipse is equal to x² / 9 + y² / 36 = 1.

In this problem we must determine the equation of an ellipse with vertices at point (0, - 6) and (0, 6) and with an eccentricity of 5 / 6. This can be done by means of the following expression:

(x - h)² / b² + (y - k)² / a² = 1

c = √(a² - b²)

Where:

First, determine the length of the minor semiaxis:

b = √(a² - c²)

b = √(6² - 5²)

b = √(36 - 25)

b = 3

Second, determine the coordinates of the ellipse by midpoint formula:

(h, k) = 0.5 · (0, - 6) + 0.5 · (0, 6)

(h, k) = (0, 0)

Third, write the equation of the ellipse:

x² / 9 + y² / 36 = 1

To learn more on ellipses: https://brainly.com/question/19507943

#SPJ1

The numerical expression 45 - 6 x 4 can be written in words as "forty-five minus six times four."

In this expression, the order of the operations dictates that we first perform the multiplication of 6 and 4, after that which subtract the end result from the number 45.

Consequently, the expression also can be simplified as follows:

45 - 6 x 4 = 45 - 24

To assess the expression, we subtract 24 from 45:

45 - 24 = 21

Therefore, the final result of the numerical expression 45 - 6 x 4, written in words, is "twenty-one."

Learn more about numerical expression:-

https://brainly.com/question/29776518

#SPJ1

The best answer is It is not possible to save any money this month without having a negative actual net income.

This is because saving money means spending less than you earn.

If the actual net income is already zero or positive, there is no room to save without spending more than the income, which would result in a negative actual net income.

Therefore, option B, C, and D are incorrect as they all suggest that it is possible to save money without having a negative actual net income, which is not possible.

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ1

The balloon's vertical distance above the ground is given as follows:

h = 10.7 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 24º, we have that:

Hence the height is obtained as follows:

tan(24º) = h/24

h = 24 x tangent of 24 degrees

h = 10.7 ft.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

a. The range of data is 37 (max: 83, min: 46).

b. The box-and-whisker plot:

Min: 46  Q1: 53  Median: 61  Q3: 68  Max: 83

---|----|----|----|----|----|----|----|----|---

46  53  61  68  83

c. The five-number summary:

Minimum (46): Lowest speed recorded.

First Quartile (Q1 - 53): 25% of the cars were traveling at 53 mph or below.

Median (61): The middle value in the dataset, meaning 50% of cars were traveling at or below 61 mph.

Third Quartile (Q3 - 68): 75% of the cars were traveling at 68 mph or below.

Maximum (83): Highest speed recorded.

d. The IQR (Q3-Q1 = 68-53 = 15) tells you the spread of the middle 50% of the speeds. It gives an idea of how varied the speeds are in the dataset.

e. Since the majority of recorded speeds (more than 50% - based on the median) are above the 50 mph speed limit, the residents should be concerned about speeding.

Read more about range here:

https://brainly.com/question/24326172

#SPJ1

Our calculation led to a P-value of .516, exceeding the predefined significance level of 0.01 which thereby disproves any evidence indicating individuals whose applications were unsuccessful came from a group whose members had higher mean ages than those who were successful.

We will use a two-sample t-test.

Unsuccessful applicants (Group 1):

n1 = 23

Mean1 (x1) = 41.6

Standard deviation1 (s1) = 14.5

Successful applicants (Group 2):

n2 = 25

Mean2 (x2) = 39.7

Standard deviation2 (s2) = 5.4

Claim: μ1 > μ2

Opposite: μ1 ≤ μ2

In order to compare the means of two independent samples, a two-sample t-test is used.

The initial step involves calculating both the pooled variance (Sp^2) and standard error (SE).

To calculate Sp^2, use the formula ((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2),

As per our specific data set regarding sample one consisting of 22 values with an average age of 41.6 years old, and sample two having 24 values averaging at 39.7 years old, we derived a pooled variance value of 120.569.

After that, employ the equation SE = √((Sp^2/n1) + (Sp^2/n2)), which yields a value of 3.685 via inputting the aforementioned values.

Using these results enables us to take the difference of the two averages divided by SE in a simplified manner giving a t-score equal to .516.

In light of this test possessing a significance level of 0.01 and utilizing only one tail, a comparison of the calculated t-score to the t-distribution table must occur; using a critical t-value of 2.410 wherein the degrees of freedom are required to be 46.

Our calculation led to a P-value of .516, exceeding the predefined significance level of 0.01 which thereby disproves any evidence indicating individuals whose applications were unsuccessful came from a group whose members had higher mean ages than those who were successful.

Read more about critical t-value here:

https://brainly.com/question/27192813

#SPJ1

The solution to the logarithmic equation log₂(x + 4) + log₂(3) = log₂(8) + log₂(2x − 5) is x = 4

Consider the logarithmic equation,

log₂(x + 4) + log₂(3) = log₂(8) + log₂(2x − 5)

We need to solve this equation for x.

Here, the base of logarithm is 2.

Applying product rule of logarithm to log₂(x + 4) + log₂(3) we get,

log₂(x + 4) + log₂(3) = log₂(3(x + 4))

So, our equation becomes,

log₂(3(x + 4)) = log₂(8) + log₂(2x − 5)

log₂(3x + 12) = log₂(2³) + log₂(2x − 5)             .......(2³ = 8)

log₂(3x + 12) = 3log₂(2) + log₂(2x − 5)

log₂(3x + 12) = (3 × 1) + log₂(2x − 5)

log₂(3x + 12) -  log₂(2x − 5) = 3

Applying power identity of logarithm to  -log₂(2x − 5) we get,

-log₂(2x − 5) = 1 / [log₂(2x − 5)]

So, our equation becomes,

log₂(3x + 12) + [1 / log₂(2x − 5)] = 3

Applying product rule of logarithm to  log₂(3x + 12) + [1 / log₂(2x − 5)] we get,  log₂(3x + 12) + [1 / log₂(2x − 5)] =  log₂[(3x + 12) / (2x − 5)]

So, our equation becomes,

log₂[(3x + 12) / (2x − 5)] = 3

Now, exponentiate both sides.

(3x + 12) / (2x - 5) = 2³

(3x + 12) / (2x - 5) = 8

(3x + 12) = 8(2x - 5)

3x + 12 = 16x - 40

13x = 52

x = 4

This is the required value of x.

Learn more about the equation here:

https://brainly.com/question/28243079

#SPJ1

The complete question is:

Solve the logarithmic equation.

log₂(x + 4) + log₂(3) = log₂(8) + log₂(2x − 5)

The voltage across a resistor with a resistance of 10Ω that has a current of 20A going through it is 200 volts.

Given that we need to find the voltage across a resistor with a resistance of 10Ω that has a current of 20A going through it,

Using the Ohm's law,

V = IR

V = 20 x 10

V = 200 Volts

Hence the voltage across a resistor with a resistance of 10Ω that has a current of 20A going through it is 200 volts.

Learn more about Ohm's law, click;

https://brainly.com/question/1247379

#SPJ1

The measure of the angle m∠ZYX of the trapezoid is equal to 139°

A trapezoid is a quadrilateral with two parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The adjacent angles of the trapezium are supplementary, so their sum is equal to 180°.

3x + 19 + x + 1 = 180°

4x + 20 = 180°

4x = 180 - 20 {collect like terms}

4x = 160

x = 160/4 {divide through by 4}

x = 40

m∠ZYX = 3(40) + 19 = 139°.

WXYZ is a trapezoid. Equation used to solve for x is (3x + 19) + (x + 1) = 180° because the angles m∠XYZ and m∠WXY are adjacent angles.

Read more about trapezoid here:https://brainly.com/question/1463152

#SPJ1

The system of equations -9x+8y = 9x and 7y+8=8x is linear.

A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.

In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).

Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).

Therefore, the system of equations is linear.

Learn more about the System of equations here:

https://brainly.com/question/12628931

#SPJ1

The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

The venn diagram represents C'  ∩ (A ∪ B).

First, the region of C is whole shaded.

Now, C is having a common part in A and B then we need the intersecting part of C with A as well as B.

Then, looking at A and B they have the common part shaded which also shows the intersection.

So, the venn diagram represents

C'  ∩ (A ∪ B)

Learn more about Venn diagram here:

https://brainly.com/question/29301560

#SPJ1

Answer:

$155

Step-by-step explanation:

15 x 7 + 50 = 155

The requried, factored form of 6x²+7x-10 is (6x - 5)(x + 2).

To factor 6x²+7x-10, we need to find two numbers whose product is -60 (the product of the coefficient of x² and the constant term) and whose sum is 7 (the coefficient of x).

Now, we can factor by grouping:

(6x² + 12x) - (5x + 10)

6x(x + 2) - 5(x + 2)

(6x - 5)(x + 2)

Therefore, the factored form of 6x²+7x-10 is (6x - 5)(x + 2).

Learn more about Factors here:

https://brainly.com/question/24182713

#SPJ1

96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

Given that, Lena must choose a number between 67 and 113 that is a multiple of 4,6, and 8.

Start listing the multiples of 4 between 67 and 113, which are 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, and 108.

We can then narrow down the list by looking for the multiples of 6, which are 72, 78, 84, 90, 96, and 102, and the multiples of 8, which are 72, 80, 88, 96, 104, and 112.

Since 96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

Therefore, 96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

Learn more about multiples of a number here:

https://brainly.com/question/10520264.

#SPJ1

Lyle will use 8 cups of shredded cheese to make five pizzas.It's important to note that the answer may vary depending on the size of the pizzas and how much cheese Lyle wants to use on each pizza. However, based on the given information, we can conclude that Lyle will need 8 cups of shredded cheese to make five pizzas.

To solve this problem, we need to first find out how much cheese Lyle uses to make one pizza, and then multiply that by the number of pizzas he wants to make.

Lyle uses 1 3/5 cups of shredded cheese to make one large pizza. To find out how much cheese he uses to make one pizza, we can add the      whole number (1) to the fraction (3/5) to get a mixed number:

1 3/5 = 8/5 cups.

Lyle uses 8/5 cups of shredded cheese to make one pizza.

To find out how much cheese Lyle will use to make five pizzas, we can multiply the amount of cheese he uses for one pizza (8/5 cups) by the number of pizzas he wants to make (5):

8/5 cups x 5 pizzas = 40/5 cups = 8 cups.

For such more questions on Lyle:

https://brainly.com/question/30422804

#SPJ11

Answer:

If we denote the unknown number as "x", then the expression representing "9 less than the unknown number" would be:

x - 9

The measure of the angle R is 116 degrees

To determine the value of the angle, we need to know the properties of a parallelogram.

These properties are;

Then, we have that the angles are;

5x - 14

116

Substitute the angles, we have;

Equate the angles

5x - 14 = 116

collect the like terms, we have;

5x = 116 + 14

add the values

5x = 130

Make 'x the subject

x = 26

Then, <R = 5(26) - 14 = 130 - 14 = 116 degrees

Learn about parallelograms at: https://brainly.com/question/10744696

#SPJ1