|2x - 1|> 7.
|7-5x|<3

Answer:

Hence, we can conclude that there is no significant evidence to conclude that the new automobile actually do average more than 42 miles per gallon.

Step-by-step explanation:

H0 : μ = 42

H1 : μ > 42

Sample size, n = 36

xbar = 42.8

Standard deviation, s = 1.2

The test statistic :

(xbar - μ) ÷ (s / sqrt(n))

(42.8 - 42) ÷ (1.2 / sqrt(36))

0.8 ÷ 0.2 = 4

Test statistic = 4

Zcritical at 95% for a one - tailed test (right tailed) = 1.645

Test statistic > Critical value ; 4 > 1.645

Since Test statistic > Critical value ; We fail to reject the Null

Hence, we can conclude that there is no significant evidence to conclude that the new automobile actually do average more than 42 miles per gallon.

The Pvalue :

P(Z < 4) = 0.99997

Since,

Pvalue > α

0.99998 > 0.05 ; We fail to reject the Null

Hence, we can conclude that there is no significant evidence to conclude that the new automobile actually do average more than 42 miles per gallon.

Answer:

1232m^3

Step-by-step explanation:

d = 14m

r = 7m

l = 25m

h = ?

h = root l^2- r^2

h = root 25^2- 7^2

h = root 625- 49

h = root 576

h = 24m

volume of cone = 1/3 pie r^2 h

= 1/3*22/7* 7*7*24

= 22*7*8

= 154*8

= 1232m^3

Answer:

1231.5 m³

Step-by-step explanation:

You have to find the height first.

using the Pythagoras rule,

hypotaneous² = base² + height²

25² = 7² + h²

576 = h²

h = √576

h = 24

Volume of cone = 1/3 π r² h

                           = 1/3 * π* 7² * 24

                           = 1231.5 m³

Answer:

answera c

Step-by-step explanation:

Answer:

Triangle A and B

Step-by-step explanation:

The lengths from triangle A is being doubled to make the lengths of triangle B. They also have the same angles.

Answer:

If you want an expression answer (Simplify):

= 7/4a - 11

If you want an answer to the variable a (Find 'a'):

7/4a - 11 = 0

7/4a = 11

a = 44/7

Step-by-step explanation:

3/4(5a - 16) - 1/3(6a - 3)

= 15/4a - 12 - 2a + 1

= 7/4a - 11

Answer:

$41

Step-by-step explanation:

Well he withdrew 1/4 of his savings which is basically 1/4 * 164

Answer:

See below

Step-by-step explanation:

5)

k/x = w - v

Multiply by x to get it out of the denominator of the fraction.

k = wx - vx

Switch the terms so they are easier to work with.

wx - vx = k

Factor x out.

x(w - v) = k

Divide by w - v to get x by itself.

x = k/w - v.

6)

ac = d - r

Divide by c to get a by itself.

a = d/c - r/c

Combine the two fractions to simplify.

a = d-r/c.

Step-by-step explanation:

3+x-2/x-3<_4

cross multiply

3+x-2<_4(x-3)

3+x-2<_4x-12

1+x<_4x-12

collect like terms

1+12<_4x-x

13<_3x

divide both side by 3

13/3<_×

6.5<_x

Answer:

35

Step-by-step explanation:

Answer:

The answer is 35

Step-by-step explanation:

5/8 x 56

5 x7 = 35

Answer:

[tex] 379 \: {units}^{2} [/tex]

Step-by-step explanation:

Area of the composite figure

= Area of rectangle with dimensions 17 & 11 units + Area of trapezoid with length of parallel sides 11 and 21 units and height (29 - 17 = 12) 12 units.

[tex] = 17 \times 11 + \frac{1}{2} (11 + 21) \times 12 \\ \\ = 187 + 32 \times 6 \\ \\ = 187 + 192 \\ \\ = 379 \: {units}^{2} [/tex]

Answer:

-The function f translated 2 units down and 3 units right. > g(x)=7x-18

-The function f stretched vertically by a factor of 3 and translated up by 2 units. > g(x)=21x+17

-The function f stretched vertically by a factor of 2 and translated down by 3 units. > g(x)=14x+7

-The function f reflected about the y-axis and translated 3 units left. >g(x)=-7x-16

Step-by-step explanation:

-A function is shifted up or down when a constant is added outside the function. If the constant is positive the function is shifted up. If the constant is negative, the function is shifted down.

-A function is shifted left or right when a constant is subtracted from the x-value inside the function. If the constant is positive, the function is shifted to the right. If the constant is negative, the function is shifted to the left.

-A function is vertically stretched or compressed when it is multiplied by a constant. If the constant is greater than one, it results in a vertical stretch. If the constant is in between zero and one, it results in a vertical compression.

-A function is reflected about the y-axis when the x-value is multiplied by a negative constant.

Answer:

The function f stretched vertically by a factor of 3 and translated up by 2 units.

g(x)=21x+17

The function f translated 2 units down and 3 units right.

g(x)=7x-18

The function f reflected about the y-axis and translated 3 units left.

g(x)=-7x-16

The function f stretched vertically by a factor of 2 and translated down by 3 units.

g(x)=14x+7

Step-by-step explanation:

Functions can be moved and re-sized by changing the parameters of the function.

A function is shifted up or down when a constant is added outside the function. If the constant is positive the function is shifted up. If the constant is negative, the function is shifted down.

A function is shifted left or right when a constant is subtracted from the x-value inside the function. If the constant is positive, the function is shifted to the right. If the constant is negative, the function is shifted to the left.

A function is vertically stretched or compressed when it is multiplied by a constant. If the constant is greater than one, it results in a vertical stretch. If the constant is in between zero and one, it results in a vertical compression.

A function is reflected about the y-axis when the x-value is multiplied by a negative constant.

Answer:

495 milliliters of the 95% mixture are needed.

Step-by-step explanation:

Given that I need a 90% alcohol solution, and on hand I have a 55 ml of a 45% alcohol mixture, and I also have 95% alcohol mixture, to determine how much of the 95% mixture will I need to add to obtain the desired solution, the following calculation must be performed:

55 x 0.45 + 45 x 0.95 = 67.5

25 x 0.45 + 75 x 0.95 = 82.5

15 x 0.45 + 85 x 0.95 = 87.5

10 x 0.45 + 90 x 0.95 = 90

10 = 55

90 = X

90 x 55/10 = X

4,950 / 10 = X

495 = X

Thus, 495 milliliters of the 95% mixture are needed.

Step-by-step explanation:

Use Sine rule.

[tex] \frac{ac}{ \sin(b) } = \frac{ab}{ \sin(c) } \\ \frac{ac}{ \sin(90) } = \frac{10}{ \sin(42) } \\ ac \sin(42) = 10 \sin(90) \\ ac = \frac{10 \sin(90) }{ \sin(42) } \\ ac = 14.9 \: units \: (3s.f)[/tex]

Angle A + angle B + angle C = 180 (sum of angles in triangle)

Angle A + 90 + 42 = 180

Angle A + 132 = 180

Angle A = 180 - 132

= 48

[tex] \frac{bc}{ \sin(a) } = \frac{ab}{ \sin(c) } \\ \frac{bc}{ \sin(48) } = \frac{10}{ \sin(42) } \\ bc \sin(42) = 10 \sin(48) \\ bc = \frac{10 \sin(48) }{ \sin(42) } \\ = 11.1units (3sf)[/tex]

Answer:

Step-by-step explanation:

You can convert 2 3/5 into 13/5 because 5/5 = 1 and 10/5 = 2.

Now that you have 13/5, you will see it’s much easier to divide! There are thirteen fifths cups of dough and he needs one fifths cups of dough for each dumpling. This means he can make 13!

Answer:

PΔJKL=66

Step-by-step explanation:

so we are given the line segments JK, KL, and LJ which are tangent to k(O), and also that JA=9, AL=10, and CK=14

JL=JA+AL (parts whole postulate)

JL=9+10=19 (substitution, algebra)

JA=JB=9 (tangent segments from the same point are congruent)

CK=KB=14 (tangent segments from the same point are congruent)

JK=JB+KB (parts whole postulate)

JK=9+14=23 (substitution, algebra)

LA=LC=10 (tangent segments from the same point are congruent)

LK=LC+CK (parts whole postulate)

LK=10+14=24 (substitution, algebra)

Perimeter of ΔJKL=LK+KL+LJ (perimeter formula for triangles)

Perimeter of ΔJKL=23+24+19=66 (substitution, algebra)

I hope this helps you

Answer:

B

Step-by-step explanation:

Sphere Surface Area = 4 • π • r²

For it to equal 16 PI, then radius must equal 2

4*PI*2*2 = 16 PI

Sphere Volume = 4/3 • π • r³

Sphere Volume = 4/3 • π • 2^3

Sphere Volume = 4/3 *PI * 8

Sphere Volume = 32 / 3 PI

Sphere Volume = 10.666 PI cubic feet AND I think that is answer B

which SHOULD read 10 (2/3) PI ft^3

Answer:

87

Step-by-step explanation:

tn= a + (n-1)d

t12 = 10 + (12-1)7

=87

Answer:

sometinng like x^2+ 10x+5

The single number is the constant and the number before the variable(x) is the coefficient

Step-by-step explanation:

Answer:

It would be the second answer, x=-3

Step-by-step explanation:

Exponents: 7-3= 4

3 to the power of 4 = 81

x=3 for both of the questions

Answer:

4.32×10^5

first calculate the left side and the calculate the right side.

finaly substract the result you get when you calculate at the first the result is 4.32 ×10^5

Answer:

Step-by-step explanation:

distributive property

12 in is 1 ft, 5 in is ~0.41 ft, 13 in is ~1.08 ft

16 oz is 1 lb, 9 oz is ~0.56 lbs, 18 oz is ~1.13 lbs

Answer:

4 feet is left in the wall

Step-by-step explanation:

If something is 1 foot and it’s supposed to be 2 feet, how much space is left? 1 foot, therefore you have to subtract what you want from what you have.

Answer:

2 ft.

Step-by-step explanation:

14 - 10 = 4.

4/2 = 2

You divide beacuse theres space on botrhsides of the painting.

Answer:

Step-by-step explanation:

0,5

Answer:

12.54kg

Step-by-step explanation:

(23/4 + 35/6 + 23/8)kg

[tex] = \frac{(23 \times 6) + (35 \times 4) + (23 \times 3)}{24} [/tex]

[tex] = \frac{92 + 140 + 69}{24} [/tex]

= 301/24

= 12.54kg