Write on equation if the slope is 3/4
and the y-intercept is -4,

Answer:

a vertical compression by a factor of 1/8

Step-by-step explanation:

Answer:

a vertical compression by a factor of \(\frac{1}{8}\)

Step-by-step explanation:

Start with the original function \(f(x) = 4^x+1\).

Apply the vertical compression by multiplying the function by  \(\frac{1}{8}\):

\(g(x) = (\frac{1}{8} ) * 4^x+1\).

Simplify the expression:

\(g(x) = \frac{1}{8} * 4^x * 4^1\).

Use the property of exponents \((a^{b+c} = a^b * a^c)\) to simplify further:

\(g(x) = \frac{1}{8} * (4^x * 4)\).

Simplify the expression inside the parentheses:

\(g(x) = \frac{1}{8} * (4^{x+1} )\).

Answer:

Answer: 855

Step-by-step explanation:

I take it you want the total number of fruit? You should state the question. I will assume I am correct.

So 25% of 60 baskets = 25/100 * 60 = 15 baskets.

Each basic contains 12 pieces of fruits                     12 * 15 = 180

And 75% of 60 baskets = 0.75 * 60 = 45 baskets.

Each contains 15 pieces                                            45 * 15 = 675

The total number of fruit in all is                                              855

Answer:

the first equation represents the problem and Lucas would have run 10 miles the second day.

Step-by-step explanation:

25 - 15 = 10 miles on the second day

The side length of AC is 6 units for the shown triangle. The correct answer would be an option (C).

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

The right triangle is given in the question, as shown.

AD = 4 cm and BD = 5

In ΔACD and ΔABC

∠ACD = ∠ABC

∠ACD = ∠BAC = 90°

∠CAD = ∠ACD (remaining)

So ΔACD and ΔABC are similar

Hence

AD / AC = AC/ BC

Apply the cross-multiplication operation, and we get

AC² = AD × BC

AC² = 4 × 9

AC² = 36

AC = 6 cm

So, the side length of AC is 6 units.

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Answer:

b = -9

Step-by-step explanation:

Axis of symmetry of a parabola = -b / 2a.

Where y = ax² + bx + c.

Given f(x) = 3x^2 + bx + 4,

a = 3, and c = 4.

If the axis of symmetry is 3/2, than b can be found by substitution and algebra.

[ x = -b / 2a ] → [ 3 / 2 = -b / 2a ] →

[ 3 / 2 = -b / 2 (3) ] → [ 3 / 2 = -b / 6 ] →

[ 3 / 2 × 6 = -b / 6 × 6 ] → [ 18 / 2 = -b ] →

[ 9 = -b ] → [ -b = 9 ] → [ (-)(-b) = (-)(9) ] →

b = -9

Answer:

Step-by-step explanation:

Let the point (6, -5) be M, and point B has coordinates of (x, y)

As the point A(7, -3) reflects over the point M, it becomes the midpoint of segment AB

Using midpoint formula, finding the coordinates of the point B

So the point B is (5, -7)

Answer:

36

Step-by-step explanation:

180-144=36

Answer:

15/16

Step-by-step explanation:

Using the order of operations, we need to multiply in the parentheses first...

3/5*25/24=75/120, which simplifies to 5/8.

Next, we need to divide 5/8 by 2/3. To divide, we can actually multiply by the reciprocal, which is flipping the fraction that you are dividing by. In this case, we need to multiply 5/8 by the reciprocal of 2/3. The reciprocal of 2/3 is 3/2, so we need to multiply 5/8 by 3/2.

5/8*3/2=15/16

This is the final answer!

I hope this helped you out!! Have an amazing day φ(゜▽゜*)♪

Answer: $9,779

Step-by-step explanation:

Where:

C is the coupon payment

r is the yield to maturity (expressed as a decimal)

n is the total number of coupon payments

F is the face value or par value of the bond

In this case, the bond has a $10,000 face value, a coupon rate of 7.60% (or 0.076 as a decimal), semiannual coupons, and a yield to maturity of 4.30% (or 0.043 as a decimal). The bond matures in five years, so there will be 10 semiannual coupon payments.

Let's calculate the price:

Answer:

12 cm is the right answer pls mark me brainliest

The height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles is 12 cm.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Heron's formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides:

Area = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.

Given:

Three sides are: 15cm, 25 cm and 2 cm

Now, Using Heron's formula

semi-perimeter= (25+ 20 + 15)/2

s= 30 cm

Now,

Area of triangle

=√s(s-a)(s-b)(s-c)

=√30* 5 * 10* 15

=√5*2*3*5*2*5*3*5

=5*5*2*3

=150 cm²

Again, area of triangle= 1/2* b* h

150= 1/2* 25* x

12cm= x

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Answer:

Step-by-step explanation:

Use the slope formula of y^2-y^1 over x^2-x^1

(-9,0)

x^1 ,y^1

(-17,4)

x^2,y^2

4-0 over -17-(-9) ----> 4/-8

Simplify 4/-8 by dividing the numerator and denominator by 4

the discount rate is 3.5% (rounded to one decimal place).

To determine the discount rate, we need to compare the present value of Option A (one-time payment) with the present value of Option B (equal annual payments). The winner is indifferent between the two options when their present values are equal.

Option A: The one-time payment is $471 million.

Option B: The winner will receive 30 equal annual payments, with the first payment made in 2020. The total amount of payments is $768.4 million, so each payment is $768.4 million / 30 = $25.613 million.

Now, we can calculate the present value of Option B using the formula for the present value of an annuity:

\(PV = PMT / (1 + r)^n\)

Where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.

Plugging in the values, we have:

$471 million = $25.613 million / \((1 + r)^{30}\)

Simplifying the equation and solving for r, we find:

\((1 + r)^{30}\) = $25.613 million / $471 million

\((1 + r)^{30}\) = 0.054427

Taking the 30th root of both sides, we get:

1 + r = (0.054427)^(1/30)

r = (0.054427)^(1/30) - 1

Calculating the value, we find that r is approximately 0.035 or 3.5%.

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False, For this situation, the professor should not use a t test with related samples.

The scenario described in the question involves two independent samples (upper and lower classmen) and not related samples. A t-test for related samples is used when the same group of participants is measured twice, resulting in paired or dependent samples.

Since the variances of the two independent samples are equal, the appropriate test in this scenario is a two-sample t-test for equal variances. However, the sample size of 10 for each group is relatively small, and the normality assumption of the t-test may not hold. Therefore, the professor should first check the normality assumption of the data using a normal probability plot or a Shapiro-Wilk test. If the assumption is not met, nonparametric tests such as the Wilcoxon rank-sum test can be used as an alternative.

In summary, the correct statistical test for this scenario is a two-sample t-test for equal variances or a nonparametric alternative if the normality assumption is not met. The t-test for related samples is not appropriate in this case.

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Answer:

\(\boxed{\checkmark}\quad x+2=\pm\sqrt{\dfrac{27}{5}}\)

\(\boxed{\checkmark}\quad 5(x^2+4x)=7\)

\(\boxed{\checkmark}\quad 5(x^2+4x+4)=7+20\)

Step-by-step explanation:

Sergey is solving the quadratic equation 5x² + 20x - 7 = 0.

To solve the quadratic equation by completing the square, begin by moving the constant to the right side of the equation by adding 7 to both sides:

\(\implies 5x^2+20x-7+7=0+7\)

\(\implies 5x^2 + 20x =7\)

The next step is to factor out the leading coefficient from the terms on the left side:

\(\implies 5(x^2+4x)=7\)

Now we need to make the terms inside the parentheses a perfect square trinomial. To do this, add the square of half the coefficient of the term in x inside the parentheses, and add the distributed value to the right side of the equation:

\(\implies 5\left(x^2+4x+\left(\dfrac{4}{2}\right)^2\right)=7+5\left(\dfrac{4}{2}\right)^2\)

\(\implies 5(x^2+4x+4)=7+20\)

Factor the perfect square trinomial on the left side and simplify the right side of the equation:

\(\implies 5(x+2)^2=27\)

Divide both sides of the equation by 5:

\(\implies \dfrac{5(x+2)^2}{5}=\dfrac{27}{5}\)

\(\implies (x+2)^2=\dfrac{27}{5}\)

Square root both sides of the equation:

\(\implies \sqrt{(x+2)^2}=\sqrt{\dfrac{27}{5}}\)

\(\implies x+2=\pm\sqrt{\dfrac{27}{5}}\)

Finally, subtract 2 from both sides:

\(\implies x+2-2=-2\pm\sqrt{\dfrac{27}{5}}\)

\(\implies x=-2\pm\sqrt{\dfrac{27}{5}}\)

Answer:

Write in slope-intercept form, \(y=mx+b\).

5. \(y=2x+7\)

6. \(y=-\frac{5}{3} x+4\)

7. \(y=x-1\)

8. \(y=\frac{1}{3}x +5\)

9. \(y=\frac{4}{5}x -2\)

10. \(y=-\frac{7}{3}x + 6\)

The probability that the sample will contain more than 5% defective units is approximately 0.9525 or 95.25%.

To solve this problem, we can use the binomial distribution formula:

P(X > 5) = 1 - P(X ≤ 5)

where X is the number of defective items in a sample of size n = 100, and p = 0.1 is the probability of an item being defective.

To calculate P(X ≤ 5), we can use the binomial cumulative distribution function (CDF) or a binomial probability table. Alternatively, we can use a normal approximation to the binomial distribution, which is valid when np ≥ 10 and n(1-p) ≥ 10, as is the case here (np = 10 and n(1-p) = 90).

Using the normal approximation, we can standardize the distribution of X as follows:

\(z = (X - np) / \sqrt{(np(1-p))}\)

Then, we can use a standard normal table or calculator to find the probability of z ≤ z0, where z0 is the standardized value corresponding to X = 5.

Let's use the normal approximation method to solve the problem:

np = 100 x 0.1 = 10

σ = \(\sqrt{(np(1-p))} = \sqrt{(9)} = 3\)

z0 = (5 - 10) / 3 = -1.67 (rounded to two decimal places)

Using a standard normal table or calculator, we find that P(Z ≤ -1.67) = 0.0475 (rounded to four decimal places).

Therefore, P(X > 5) = 1 - P(X ≤ 5) = 1 - 0.0475 = 0.9525 (rounded to four decimal places).

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Answer: p - 1 > 6, or p > 7

Step-by-step explanation:

   We will write an expression from the sentence given.

difference of a number (p) and 1 ➜ p - 1

is greater than ➜ >

    The difference of a number p and 1 is greater than 6​ ➜ p - 1 > 6

   To solve for the possible values of p, we will add 1 to both sides of the equation;

p > 7

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The distance of the drinking fountain from the bench is 42.7 feet.

From the graph in the given figure we can see that,

The coordinates of the point F are = (-6, 1)

The coordinates of the point B are = (2, 4)

The distance between the points F and B is given by

= √[(2 - (-6))² + (4 - 1)²]

= √[(2 + 6))² + (4 - 1)²]

= √[(8)² + (3)²]

= √[64 + 9]

= √73 units

1 unit in the graph is equal to 5 feet.

So the √73 units is equal to = √73 * 5 = 42.7 feet. [Rounding off to nearest tenth]

Hence the distance of the drinking fountain from the bench is 42.7 feet.

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The question is incomplete. The complete question will be -

The course of action that can be taken to help the economy is through the expansionary fiscal policy involving cuts to individual tax rates and increased

investments in infrastructure could be used to strengthen the economy. That is option B.

The inflation of economy of a country is defined as the sudden rise in the cost of goods and services which affects the lives of the citizens of the country.

The common causes of economic inflation include the following:

The policy that can be used to help the economy of a country is the expansionary fiscal policy.

This policy involves cutting individuals tax rates, increasing investment in infrastructure which can help strengthen the economy of the country.

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Answer:

Step-by-step explanation:

4(3n- 5) =

12n - 20

Rounded to the nearest thousand, the farmer needs approximately 876,000 corn plants to maximize the yield for the field represented on the coordinate grid.

To determine the number of corn plants the farmer needs, we first need to calculate the area of the field represented on the coordinate grid. Given that each unit on the grid represents one foot, we can find the area in square feet.

The grid appears to be a square with sides measuring 1000 feet each. Therefore, the area of the field is: Area = side^2 = 1000 ft * 1000 ft = 1,000,000 square feet. Since 1 acre is equal to 43,560 square feet, we can now calculate the number of corn plants needed at a density of 38,000 plants per acre.

Number of corn plants needed = (Area in square feet) / (Density of plants per acre). Number of corn plants needed = 1,000,000 ft^2 / 43,560 ft^2/acre * 38,000 plants/acre. Number of corn plants needed ≈ 876,110 plants.

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Answer:

12960

Step-by-step explanation:

(30+2)*405

405*30 + 405*2

12150+810

12960

Hope this helps plz hit the crown :D

Answer:

Step-by-step explanation:

∠EAD = ∠CAB = 53°

By Side-angle-side, △EAD is congruent to △CAB

∠E = 96°

∠D = 180-96-53 = 31°

x = 31°

A. The distance from the x - axis to the top of the circle is 10.3 feet

B. The equation of the circle is (x - 2)² + (x² - 3)² = 4

C. The equation of the parabola is x = a(y - k)² + h

D. The area of the window is 9.2 ft²

A. (14.6 - x)² + (4.6/2)² = 10.6 { Pythagores theorem"}

(14.6 - x) + 5.29 = 112.36

(14.6-x)² = 112.36 - 5.29

14.6-x)²= 107.07

(14.6 - x)² = 107.07

X= 213.16 - 107.07

x = 106.09

X=10.3 feet

B. The equation of the circle is (x - 2)² + (x² - 3)² = 4

The equation represents a circle centered at the point (2, 3) with a radius of 2 units, as determined by the standard form equation of a circle:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

C. The equation of the parabola is x = a(y - k)² + h

D. The area of the window is determined using the following below:

x = a(y - k)² + h, where a is the horizontal stretch or compression factor.

x = 14.6 (10.1 - 4.6)² + 4.6

x = (147.47 - 67.16)² + 4.6

x = 80.31)² + 4.6

x = 84.37²

x = 9.2 ft

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Answer:

-2.46

Step-by-step explanation:

151/24=6.29

6.29-8.75=-2.46

Answer:

-2.45833333333

Step-by-step explanation:

151 divided by 24= 6.29166666667

6.29166666667-8.75=-2.45833333333

2dp=2.46

The number of volunteers who worked more than 15 hours can be found by summing up the frequencies

of the bars in the histogram that represent the groups with more than 15 hours of community service.

To determine how many volunteers worked more than 15 hours using the given histogram.

Identify the section of the histogram that represents volunteers who worked more than 15 hours.

Read the height (frequency) of the bars representing the groups of volunteers with more than 15 hours of community

service.

Add the frequencies of these bars to get the total number of volunteers who worked more than 15 hours.

In conclusion, the number of volunteers who worked more than 15 hours can be found by summing up the frequencies

of the bars in the histogram that represent the groups with more than 15 hours of community service.

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Answer:

2x18=36

im not sure if that's what you meant but i can answer again if you want

Step-by-step explanation:

Answer:

sin ( 330 )

 csc  ( 60 )

cos  ( 390 )

Step-by-step explanation:

Answer:

Step-by-step explanation:

Cos(theta) = adjacent / hypotenuse.

Adjacent = 29

Hypotenuse = 31

Cos(theta) = 29/31

Cos(theta) = 0.5355

theta= cos-1(0.5355)

theta = 20.69

Answer: (Rounded) = 21

Answer:

this should be the answer 4x^3 & 2x^2