4.
Evaluate the function rule for the given value. y = 4 • 2^x for x = –6

A. –48
B. 1/8
C. 1/16
D. 1/32

Answer:

n = -1

Step-by-step explanation:

→The fraction \(\frac{n}{5}\) is really just \(\frac{1}{5}n\):

\(\frac{1}{5}n = \frac{-1}{5}\)

→To get n by itself, you must multiply both sides by the reciprocal of \(\frac{1}{5}\), which is 5:

5 · \(\frac{1}{5}n = \frac{-1}{5}\) · 5

n = -1

The roots of the equation 25x² + 60x + 37 = 0 in simplest form will be - 6/5 + 100i and - 6/5 - 100i.

Let the equation be ax² + bx + c = 0.

Then the roots of the equation will be

\(\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}\)

The equation is given below.

25x² + 60x + 37 = 0

The roots of the equation is given as,

x = [- 60 ± √{(60)² - 4 × 25 × 37}] / (2 × 25)

x = [- 60 ± √(-100)] / 50

x = [- 60 ± 100i] / 50

x = - 6/5 ± 100 i

x = - 6/5 + 100i, - 6/5 - 100i

The roots of the equation 25x² + 60x + 37 = 0 in simplest form will be - 6/5 + 100i and - 6/5 - 100i.

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The speed of the walker is 16.67 miles per hour.

The speed of the cyclist is 25 miles per hour.

Let the speed of a walker = x

Biker's speed = 1.5x

Their relative speed will be:

= 1.5x - x = 0.5x

Distance between them = 12.5 miles

Time taken = 1.5 hours.

It should be noted that distance will be:

= Speed × Time

12.5 = 1.5 × 0.5x

Divide through to get x

12.5 = 0.75x

x = 16.67 miles per hour.

Speed of cyclist = 16.67 × 1.5 = 25 miles per hour.

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4/5

This is because there are 5 rectangles in total, but only 4 out of the 5 rectangles are colored.

Answer:

Step-by-step explanation:

The boxes filled in green represent the numerator: 4

The total number of boxes represent the denominator: 5

Therefore the picture represents 4 out of 5 boxes full, or 4/5.

The function h is given by h(x) = log2(x^2). The positive value of x for which h(x) = 3 is 2√2.

To solve this, we can start by setting h(x) equal to 3:

log2(x^2) = 3

Next, we can rewrite the equation in exponential form:

2^3 = x^2

Simplifying, we get:

8 = x^2

To solve for x, we can take the square root of both sides:

√8 = √(x^2)

Simplifying further:

√8 = x

However, we need to find the positive value of x. So, the answer is:

x = √8

Now, let's simplify √8. Since 8 can be written as 4 * 2, we have:

x = √(4 * 2)

Taking the square root of 4 and 2 individually:

x = √4 * √2

Simplifying:

x = 2 * √2

Therefore, the positive value of x for which h(x) = 3 is 2√2.

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Answer:

Step-by-step explanation:

Part A:

car 1 => exponential function

car 2=> linear function

Part B:

car 1 => the function f(x) = 45,000 • (0.9)^x

car 2= > the function f(x) = 45,000 – (3,000)x

Part C:

after 13 years, the value of :

car 1 => 45,000 • (0.9)^13 = $ 11,438.40

car 2=> 45,000 – (3,000)(13) = $ 6,000

the difference is = 11,438.40 – 6,000= $ 5,438.40

she should buy 1

The function describing the value of car 1 is exponential and that of car 2 is linear. The function for car 1 is \(f(x) =\) \(45000 (9/10)^x\) and the function for car 2 is \(f(x) = 45000 - 3000x\).

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Part A :

If a function is linear, then the function values have equal differences.

If a function is exponential, the function values have equal ratios.

For car 1 :

36450 / 40,500 = 9/10

32805 / 36450 = 9/10

Values of car have equal ratios.

This is exponential function.

For car 2 :

39000 - 42000 = -3000

36000 - 39000 = -3000

Values of car have equal differences

This is linear function.

Part B :

The initial value of car is 45,000.

For car 1 :

\(f(x) =\) \(45000 (9/10)^x\)

f(1) = 40,500, f(2) = 36,450, ............

For car 2 :

\(f(x) = 45000 - 3000x\)

f(1) = 42,000, f(2) = 39,000, ..........

Part C :

For car 1 :

f(13) =  \(45000 (9/10)^{13\) = 11438.396

For car 2 :

f(13) = \(45000 - (3000*13)\) = 6000

There is a significant difference in the values of the car after 13 years. The value of the car 1 is greater.

Hence the value of the car 1 is described by an exponential function and that of car 2 by linear function. The value of car 1 is greater after 13 years.

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Answer:

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = - 120\)

Step-by-step explanation:

By the rule of Integer multiplications,

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = [ (-1) \times (-2) ] \times [(-3) \times (-4)] \times (-5)\)

                                                      \(= [2] \times [12] \times (-5)\)

                                                      \(= -120\)

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Answer: see below

Step-by-step explanation:

They intersect at the point (2,6) which is the solution

Given that, The 99% confidence interval of a population mean is (1,7). We need to find the 95% confidence interval.As the confidence interval becomes wider as the confidence level increases. Hence, the 95% confidence interval will have a greater range than the 99% confidence interval.Confidence interval can be calculated by the formula:Confidence Interval = $\overline{X}$ ± Zα/2 (σ/√n)Where, $\overline{X}$ is the sample mean.Zα/2 is the critical valueσ is the population standard deviationn is the sample sizeNow, Zα/2 for 99% confidence interval is 2.576 as per the normal distribution table.In the same way, Zα/2 for 95% confidence interval is 1.96.Converting the above formula for 95% confidence interval:1.96 = (1,7 - $\overline{X}$)/(σ/√n)On solving the above equation, we get: σ/√n = 0.2039σ = 0.2039 √n.....(1)Also, (1,7 - $\overline{X}$)/σ = 1.96....(2)Substituting equation (1) in equation (2), we get:(1,7 - $\overline{X}$)/ (0.2039√n) = 1.96On solving this equation, we get:$\overline{X}$ = 1.47 √n + 1.7...........(3)Now, for option (a), (b), (c) and (d), we need to verify which option satisfies the equation (3).Let's check for option (a):(2+6)/2 = 4............taking the average1.47 √n + 1.7 = 4n = 19.22 squaring both sidesn = 363.6Hence, option (a) is the correct answer.Write the answer in main part:The 95% confidence interval is (2,6).Explanation:On solving the equation, we get that the option (a) is correct. Therefore, the 95% confidence interval is (2,6).Conclusion:Therefore, option (a) (2,6) is the correct 95% confidence interval.

The 95% confidence interval for the population mean is given as follows:

c) (2,6).

The 99% confidence interval for the population mean is given as follows:

(1,7).

Hence the sample mean is given as follows:

(1 + 7)/2 = 4.

Meaning that the mean of the two bounds in the interval must be of 4.

The 95% confidence interval is narrower than the 99% confidence interval, hence, considering the mean of the bounds of 4, option c is the correct option for this problem.

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Charlie

Here, we want to check if polynomials is closed under subtraction or not

To check this, we proceed either ways, if the answer is same, then it is closed. If otherwise, then it is not

We have;

As we can see, both results are not equal

If subtraction was closed under polynomials, then the results of both should have been equal. This means Charlie is correct.

Answer:

$1.15

Step-by-step explanation:

add the cost of all of the items: 1 + 3.50 + 3.50 + 1 = 9

multiply 9 by the given discount: 9 x 0.15 = 1.35

you get 1.15, this is the dollar price of the discount

Answer:

C, 1.35

Step-by-step explanation:

Let's add the prices of the items together first since they got 15% off when they bought it together.

1 + 3.50 + 3.50 + 1 = 9

Next, we will do 15% off of 9.

15% x 9 =

(15:100) x 9 =

(15 x 9):100 =

135:100 = 1.35

Answer:

5

Step-by-step explanation:

If there are 13 baseballs in a box and 8 in a bag, subtract 8 from 13 and you get 5 baseballs. So in total there are 5 more baseballs in the box than the bag.

Answer:

A

Step-by-step explanation:

i got (4,4) so it may be A hope it help.

Divide by 3

Equating

Now

C

Answer:

C.  y = 20

Step-by-step explanation:

Given system of equations:

\(\begin{cases}3y = 18x + 6\\y = 2x + 14\end{cases}\)

Multiply the second equation by 3:

\(\implies (3)y=(3)2x+(3)14\)

\(\implies 3y=6x+42\)

Subtract this from the first equation to eliminate 3y:

\(\begin{array}{r l}3y & = 18x+6\\-\quad3y&=6x+42\\\cline{1-2}0&=12x-36\end{array}\)

Solve the resulting equation for x:

\(\implies 12x-36=0\)

\(\implies 12x=36\)

\(\implies x=3\)

Substitute the found value of x into the original second equation and solve for y:

\(\implies y=2(3)+14\)

\(\implies y=6+14\)

\(\implies y=20\)

The percentage change in the number of voters who approved of the senators performance would be = 8.9%

The percent change of a number is defined as the expression that shows if a number is increased or decreased when compared with its original value and multiplied by 100.

q

The number of voter per poll = 1000

The number of individuals that approved of senator last year = 513

The number of individuals that approved of senator this year = 429.

The difference between the two years = 513-429 = 84

The total people that approved = 942

The percentage difference = 84/942 ×100/1

= 8400/942

= 8.9%

This shows that there is an 8.9% decrease in the number of individuals that approved of the senators performance this year than last year.

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Answer:

they have lost 10 yards

Step-by-step explanation:

12-5+3=10

Answer:c x=13

Step-by-step explanation:

straight line =180

180-50=130

7x+3x=10x

130/10=13

So the answer is x=13

The equation that we can be able to use in this case is d = 45h.

The equation of a straight line is typically represented in slope-intercept form, which is given by:

y = mx + b

By knowing the slope (m) and the y-intercept (b), you can write the equation of a straight line. The slope represents how much y changes for a given change in x, while the y-intercept determines where the line crosses the y-axis.

We know that the slope of the line can be found from;

m = \(y_{2} - y_{1} /x_{2} - x_{1}\)

m = 90 - 45/2 - 1

= 45

Then we have that;

d = 45h

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1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

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Answer:

\((2,2)~ \text{and}~ (-2,-2)\)

Step by step explanation:

\(x^2 +y^2 =8~~~~~~...(i)\\\\x-y=0~~~~~~~~~...(ii)\\\\\text{From (ii):}\\\\x-y = 0 \implies x = y\\\\\text{Substitute x = y in eq (i):}\\\\~~~~~~y^2 +y^2 =8\\\\\implies 2y^2 = 8\\ \\\implies y^2 = \dfrac 82\\\\\implies y^2 = 4\\\\\implies y = \pm\sqrt 4\\\\\implies y = \pm 2\\\\\text{Substitute y = x in equation (i):}\\ \\~~~~~~x^2 +x^2 = 8\\ \\\implies 2x^2 = 8\\\\\implies x^2 = \dfrac 82\\\\\implies x^2 = 4\\\\\implies x = \pm\sqrt 4\\\\\implies x = \pm2\\\\\)

\(\text{Hence,}~ (x,y) = (\pm2, \pm 2)\)

Answer:

12 bags of cookies.

Step-by-step explanation:

Since you already start out with $24, you will have a y-intercept of 24. Your slope will be 3, since each bag sells for $3.

Your equation will be y = 3c + 24.

Your sister does not start out with money, so she will have a y-intercept of 0. Her slope will be 5, as each bag sells for $5.

Her equation will be y = 5c.

Since y = y, you can set the two equations equal to each other.

3c + 24 = 5c

5c = 3c + 24

Subtract 3c from both sides

2c = 24

Divide both sides by 2

c = 12

So, they must sell 12 bags of cookies to raise the same amount of money, $60. Yum!

Hope this helps!

Answer:

I wish I could help  but i did not learn this  yet

Step-by-step explanation:

This is read as the set of all possible combinations of Heads and Tails, combined with the set of all odd numbers from 1 to 5.

A.

Sample Space:

{Heads, Tails} x {1, 2, 3, 4, 5}

B. Favorable Outcomes: {Heads, 1}, {Heads, 3}, {Tails, 1}, {Tails, 3}, {Tails, 5}

A. The sample space for this event can be represented as a set of all possible outcomes, which can be written as {Heads, Tails} x {1, 2, 3, 4, 5}. This is read as the set of all possible combinations of Heads and Tails, combined with the set of all numbers from 1 to 5.

B. The favorable outcomes for the event of choosing an odd number are {Heads, 1}, {Heads, 3}, {Tails, 1}, {Tails, 3}, {Tails, 5}. This is read as the set of all possible combinations of Heads and Tails, combined with the set of all odd numbers from 1 to 5.

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The equation that shows the different and incorrect relationship is C. b = ✓(a² + c²)

It should be noted that from the information the Pythagoras theorem was illustrated and given as c² = a² + b²

Therefore, the equations that can be gotten from it include b² = c² - a².

It should be noted that the equation that shows the different and incorrect relationship is b = ✓(a² + c²)

In conclusion, the correct option is C.

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Answer: the one in the bottom right

Step-by-step explanation: each month which is the x axis ( the bottom line) the y axis (line on the left) goes up by 5

so when the x axis is 1 the y axis should be at 5

Answer:Given points are (6, -2) and (12, -2). Find the slope of the line using the formula m = (y2 - y1)/(x2 - x1) Here, y1 = -2, y2 = -2, x1 = 6 and x2 = 12

⇒ m = (-2 - -2)/(12 - 6) = 0/6 = 0

Step-by-step explanation: i hoped i helped a little :)

Consider a circle with diameter AB, and let C be a point on AB such that 2 * AC < BC. To prove that angle ABC is acute, we can use the fact that the longest side of a triangle is opposite the largest angle. By comparing the lengths of sides AB and BC, we can determine the relationship between angle ABC and its complement, angle ACB.

Since AC is shorter than BC (2 * AC < BC), we know that side BC is longer than side AC. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, AC + BC is greater than AB.

Using the fact that the longest side of a triangle is opposite the largest angle, we can infer that angle ABC is larger than angle ACB. Since angle ACB is a right angle (as it is formed by the diameter AB and a chord), angle ABC must be acute because it is larger than the right angle ACB.

Therefore, we can conclude that angle ABC is acute based on the given conditions. The proof relies on the triangle inequality theorem and the properties of angles formed by a diameter and a chord in a circle.

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Answer:

x^70

Step-by-step explanation:

When multiplying exponents, you just add them up.

x^56+14= x^70

Answer:

she makes 782p = £7.82 an hour

Step-by-step explanation:

The amount made by Ellie if She makes at least 17 hats per hour, She is paid 46p for each hat she makes, is  £7.82.

The symbols cross (×), asterisk (*), and dot (·) are used to denote multiplication. You most frequently utilize the cross when writing in your notebooks. In computer languages and algebra, the asterisk and dot are both utilized (higher mathematics).

Given:

Ellie makes at least 17 hats per hour, She is paid 46p for each hat she makes,

Calculate the amount earned by Ellie as shown below,

The amount earned by Ellie = number of hats  × price of one hat

The amount earned by Ellie = 17 × 46

The amount earned by Ellie = 782p

Convert  into Stirling pound as shown below,

The amount earned by Ellie = £7.82

Thus, the amount made by her is £7.82.

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The complete question is:

Ellie makes hats. She makes at least 17 hats per hour. She is paid 46p for each hat she makes. Find the total amount she made.