Simplify.
(29 × 35) x (24 x 3)²
A
B
C
D
620
624
213 × 37
2¹7 x 37
D

Answer:

The value of g(f(-3) would be -9

The correct conclusion is: Reject H0.

There is convincing evidence that the distribution of customer opinion is not equally distributed across the three options.

To make a conclusion based on the given information, we compare the p-value (between 0.02 and 0.025) with the significance level α = 0.05.

In hypothesis testing, if the p-value is less than the significance level, we reject the null hypothesis (H0); otherwise, we fail to reject the null hypothesis.

In this case, since the p-value is between 0.02 and 0.025, which is less than α = 0.05, we can conclude that the p-value is statistically significant. Therefore, we reject the null hypothesis (H0).

The correct conclusion is:

Reject H0.

There is convincing evidence that the distribution of customer opinion is not equally distributed across the three options.

This means that the survey results provide significant evidence to suggest that the opinions of customers are not equally distributed among the options of "approve," "disapprove," and "no opinion" after the product recall.

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Answer:

20

Step-by-step explanation:

good luck!!

Answer:

24 or 20

Step-by-step explanation:

The Answer is -0.985

I just took the test.

Answer:

Answer to your question ; f(t) = 55 = 4t

Answer:

C -1

Step-by-step explanation:

in such a case the simplest way is to simply try the 4 numbers and see :

x² - 3x - 4 = |x + 3| - 2

x² - 3x - 2 = |x + 3|

A x = -4

(-4)² - 3×-4 - 2 = |-4 + 3|

16 + 12 - 2 = 1

26 = 1

wrong.

B x = -3

(-3)² - 3×-3 - 2 = |-3 + 3|

9 + 9 - 2 = 0

16 = 0

wrong.

C x = -1

(-1)² - 3×-1 - 2 = |-1 + 3|

1 + 3 - 2 = 2

2 = 2

correct.

D x = 4

4² - 3×4 - 2 = |4 + 3|

16 - 12 - 2 = 7

2 = 7

wrong.

Answer:

(0,1)

Step-by-step explanation:

Rational numbers are numbers that can be written as the ratio of

The matrix is 3 × 3 square matrix . Its values are:

\(a_{11} = 50 \\ a_{12} = 44 \\a_{13} = -43 \\a_{21} = 31 \\a_{22} = 16 \\a_{23} = 7 \\a_{31} = 37 \\a_{32} = 119 \\a_{33} = 94\)

Given,

Matrix A and Matrix B

Now,

According to matrix multiplication rule first row of one matrix will be multiplied with first column of second matrix if the columns in first matrix is equal to the rows of second matrix.

So,

Apply multiplication rule,

\(a_{11} = 30 + 14 + 6 = 50 \\ a_{12} = 55 + 7 - 18 = 44 \\a_{13} = -20 -35 + 12 = -43 \\a_{21} = 24 - 2 + 9 = 31 \\a_{22} = 44 -1 -27 = 16 \\a_{23} = -16 + 5 + 18 = 7 \\a_{31} = 36 + 16 - 15 = 37 \\a_{32} = 66 + 8 + 45 = 119 \\a_{33} = -24 -40 -30 = -94\)

Thus the values of the matrix can be calculated.

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The sequence is:

6, 18, 54, 162.......

By proper observation of the sequence above, you would notice that there is a common ratio of 3.

That is, r = 18 / 6 = 54 / 18 = 162 / 54 = 3

Common ratio, r = 3

The first value in the sequnce is a = 6

Since the sequnce has a common ratio, it is a geometric sequence.

The formula for the nth term of a Geometric sequence is:

To get the 13th term of the sequnce, n = 13

Answer:

( −∞,−5) interval notation, and inequality solution y < -5 ,

Step-by-step explanation:

Answer:

y<-5

Your Interval Notation would be an open circle and the arrow would be pointing to the left. (<-- (-6) --- (-5) --- (-4) -->) This will be your # line.

Step-by-step explanation:

9y+5(y+3) < 4y-35

1) Distribute the 5 in 5(y+3).

9y+5y+15 < 4y-35

2) Combine like terms. 9y and 5y.

9y+5y= 14y

14y+15 < 4y-35

3) MY TIP is to keep the variables on the left side, bc if you don't at the end you will have to flip the sign. so.. Subtract 4y from both sides

14y+15 < 4y-35

-4 -4

10y+15 < -35

3) Then you will subtract 15 from both sides

10y+15 < -35

-15 -15

10y < -50

4) Last is to divide to get your variable by itself.

10y < -50

÷10 ÷10

Answer : y < -5

Interval Solution: Open circle, -5 in the middle of the line and you will shade in the numbers to the left. .

Answer:

y = \(\sqrt{55}\)

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(altitude)² = product of parts of hypotenuse

then

y² = 11 × 5 = 55 ( take square root of both sides )

y = \(\sqrt{55}\)

Answer:

domain : - ∞ < x < 1

Step-by-step explanation:

the function is increasing on the upward part of the curve. that is

from negative infinity to the vertex at (1, 3 )

domain : - ∞ < x < 1

The result of 1/11 in the base 10 system is given as is 0.09.

To visualize the long division of 1 ÷ 11 in a base ten system:

Set up the long division: 11 outside and 1.00 inside the division bracket.

Place the decimal point in the quotient above the dividend's decimal point.

Bring down the first digit (0) and divide 11 into 10; it goes 0 times.

Subtract the product (0) from 10, leaving 10.

Bring down the next digit (0) and divide 11 into 100; it goes 9 times.

Subtract 99 from 100, leaving a remainder of 1.

The result is 0.09.

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For the function f(x) = 7/8x² - 14, the x-intercepts are x = -4 and x = 4.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the x-intercepts of the function f(x), we need to solve the equation f(x) = 0.

f(x) = 7/8x² - 14

Substitute f(x) with 0 -

0 = 7/8x² - 14

Add 14 to both sides -

7/8x² = 14

Multiply both sides by 8/7 -

x² = 16

Take the square root of both sides -

x = ±4

Therefore, the x-intercepts of the function f(x) are x = -4 and x = 4.

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Answer:

The radius is 15 inches

Answer:

Shown from explanation below.

Step-by-step explanation:

If they both eat 5/12 each, it means they would both eat;

5/12 + 5/12 = (5 + 5)/12 = 10/12 = 5/6 of a bar.

Answer:

5/12 per brother x 3/1 brothers = 15/12 chocolate bars ate so the brothers ate 15/12 chocolate bar because each brother ate 5/12 and there are 3 brothers so we multiply

15/12 = 1 1/4 = 5/4

Step-by-step explanation:

Answer:

The length of the rectangle (l) = 10 cm

The width of the rectangle (w) = 7 cm

Step-by-step explanation:

Step(i):-

Let 'x' be the length of the rectangle

Given that the width is 3 feet shorter than the length

The width of the rectangle = x -3

Area of the rectangle = length × width

Step(ii):-

Area of the rectangle = length × width

                                  = x ( x-3)

Given that the area of the rectangle = 70 square feet

                       x ( x-3) = 70

              ⇒   x² - 3x - 70 =0

              ⇒  x² - 10 x + 7 x - 70 =0

             ⇒  x (x -10) +7( x-10) =0

            ⇒ ( x+7) ( x-10) = 0

           ⇒  x =-7 and x=10

Final answer:-

we choose x=10

The length of the rectangle (l) = 10 cm

The width of the rectangle (w) = 7 cm

Answer:

The tightened spot is 10 feet away from the foot of the pole.

Step-by-step explanation:

1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.

2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.

⭐What is the Pythagoras' Theorem?

3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.

Let B= the distance from the tightened spot to the foot of the pole.

\((C)^2 = (A)^2 + (B)^2\)

\(26^2 = 24^2 + B^2\)

\(676 = 576 + B^2\)

\(100 = B^2\)

\(\sqrt{100} = \sqrt{(B)^2}\)

\(10 = B\)

∴ The tightened spot is 10 feet away from the foot of the pole.

Diagram:

The equation of the line in slope - intercept form is -

y = - 5x + 77.

The equation of a straight line in slope - intercept form is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation as -

77 - y = 5x

We have the equation in the slope - intercept form as -

77 - y = 5x

y = 77 - 5x

y = - 5x + 77

Therefore, the equation of the line in slope - intercept form is -

y = - 5x + 77.

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                  = Answer:

Step-by-step explanation:

interest= 3500 * 6 * 6.9* 1/100

                  = 4949

Final value = £ 3500 + 1449

                  = 4949

Principal=P=3500

Time=T=6years

Rate of interest =R=6.9

Interest be I

\(\\ \sf\longmapsto I=\dfrac{PRT}{100}\)

\(\\ \sf\longmapsto I=\dfrac{3500(6)(6.9)}{100}\)

\(\\ \sf\longmapsto I=\dfrac{144900}{100}\)

\(\\ \sf\longmapsto I=1449\)

Now

Final value=3500+1449=4949

Answer:

36 individual white socks

38 individual black socks

Step-by-step explanation:

Pairs of socks = 74

He has 1 more pair of white socks than black socks.

Take the colors of the socks to be white and black

Let

Black pairs of socks = x

White pairs of socks = x + 1

Individual socks of each color

A pair of white socks = 2 Individual white socks

= 2white

A pair of black socks = 2 individual black socks

= 2black

Total pairs of socks = black pairs of socks + white pairs of socks

74 = 2white + 2black

74 = 2(x) + 2(x +1)

74 = 2x + 2x + 2

74 = 4x + 2

Subtract 2 from both sides

74 - 2 = 4x

72 = 4x

Divide both sides by 4

x = 72/4

= 18

x = 18

Pairs of white socks = x = 18

A pair of white socks = 2whites

= 2(18)

= 36 individual white socks

Pairs of black socks = x + 1

= 18 + 1

= 19 pairs

A pair of black socks = 2black

= 2(19)

= 38 individual black socks

The amount Siya will spend on tiles is given by the expression (1.1 x T / 6) x R234, where T represents the required number of tiles. To calculate the amount Siya will spend on tiles, we need to determine the number of boxes of tiles he needs to purchase and then multiply it by the price per box.

First, we need to determine the number of tiles required. Let's assume the required number of tiles is represented by the variable "T."

Since the builder recommends buying 10% more tiles in case of breakages, Siya needs to purchase 110 percentage of the required number of tiles. This can be calculated as:

110% of T = 1.1 x T

Next, we need to convert the number of tiles into the number of boxes required. We know that one box contains 6 tiles, so the number of boxes Siya needs to purchase is:

Number of boxes = (1.1 x T) / 6

Finally, we can calculate the total cost by multiplying the number of boxes by the price per box:

Total cost = (1.1 x T / 6) x R234

Please note that without knowing the specific number of tiles required (T), we cannot provide an exact amount Siya will spend.

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It looks like the integral in polar coordinates is given to be

\(\displaystyle\int_{\pi/2}^\pi \int_0^2 r^3\sin(\theta)\cos(\theta)\,\mathrm dr\,\mathrm d\theta\)

Converting back to Cartesian, we take

x = r cos(θ)

y = r sin(θ)

dx dy = r dr dθ

so we can easily recover the integrand in Cartesian:

\(r^3\sin(\theta)\cos(\theta)\,\mathrm dr\,\mathrm d\theta = (r\sin(\theta))(r\cos(\theta))(r\,\mathrm dr\,\mathrm d\theta) = xy\,\mathrm dx\,\mathrm dy\)

This leaves us with the limits:

• π/2 ≤ θ ≤ π corresponds to the second quadrant of the (x, y)-plane (that is, where x < 0 and y > 0)

• 0 ≤ r ≤ 2 correspond to the disk of radius 2 centered at the origin

Taken together, we see the region of integration is a quarter-disk of radius 2 in the second quadrant, which we can capture by the set

{(x, y) : -√2 ≤ x ≤ 0 and 0 ≤ y ≤ √(2 - x ²)}

So, in Cartesian coordinates, the integral would be

\(\displaystyle \boxed{\int_{-\sqrt2}^0 \int_0^{\sqrt{2-x^2}} xy\,\mathrm dy\,\mathrm dx}\)

a) The angles outside the side PQ measure 65° and 25°

The angles outside the side QR measure 85° and 95°

The angles outside the side PR measure 55° and 35°

b) The arc PR, PQ and PR measure 120°

a)

Let us assume that the inscribed square be ABCD and equilateral triangle is PQR.

Let side PR of triangle intersects the quadrilateral at points M and N.

So, we get a triangle DMN outside the equilateral triangle.

Here, ∠DMN = 55°, ∠D = 90°

So, ∠MND = 180 - (90 + 55)

                 = 35°

Similarly,  side PQ of triangle PQR intersects the quadrilateral at points X and Y.

So, we get a triangle AXY outside the equilateral triangle.

From triangle PXM we get the measure of angle PXM which is 65 degrees.

As angle PXM and angle AXY are opposite angles, the measure of angle AXY = 65°

∠A = 90°

So, ∠AYX = 180° - (∠A + ∠AXY )

                 = 180° - (90° + 65°)

                 = 25°

Let the side QR of triangle PQR intersects the quadrilateral at points L and K.

so we get new quadrilateral LKBC

In this quadrilateral ∠B = 90°, ∠C = 90°

From triangle QYL, we get the measure of angle QLY = 95°

So, the measure of ∠KLB = 95° .......(∠QLY and ∠KLB opposite angles)

So, the remaining angle LKC of quadrilateral LKBC would be,

∠LKC = 360° - (∠B + ∠C + ∠KLB)

∠LKC = 360° - (90 °+ 90° + 95°)

∠LKC = 85°

b)

We know that he angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

so, the measure of arc PR = 120°

the measure of arc PQ = 120°

the measure of arc RQ = 120°

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Answer:

1) Yes, it is a right angle triangle

2)Yes, it is a right angle triangle

3) No, they are not similar.

Step-by-step explanation:

Dimension of triangle A = 48, 55 & 73

Dimension of triangle B = 36, 77 & 85

For any of the triangles to be a right angled one, then;

c = √(a² + b²)

Where a,b & c are side dimensions of a triangle.

Thus;

Triangle A: c = √(48² + 55²)

c = √5329

c = 73

This tallies with what we are given and so it is a right angled triangle.

Triangle B: c = √(36² + 77²)

c = √(7225)

c = 85

Similar to the third side dimension of 85, thus it is true.

For Triangle A & B to be similar, the ratio of the 3 corresponding sides must be in a whole number ratio.

Thus, we have;

48/36 = 1.5

55/77 = 5/7

73/85 = 73/85

Since the ratios are not similar, then we can say that the triangles are not similar.

Answer:

I think 21

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(8+[16/(17-16)+11-8]\times5\\\\8+\left(\frac{16}{17-16}+11-8\right)\times \:5\\\\\left(\frac{16}{17-16}+11-8\right)\times \:5=95\\\\=8+95\\\\=103\)

Answer:

8+[16/(17-16)+11-8]x5

8 + [ 16/1 + 11 - 8 ] * 5

8 + [ 16 + 11 - 8] * 5

8 + [ 27 - 8 ] * 5

8 + 19 * 5

8 + 95

103