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Answer: first one is x≥-8 second one is x<6

Step-by-step explanation: for the first one you divide both sides by 7 and the second won do the same except divide by 9 on each side

Hello,

7x ≥ -56

⇔ 7x / 7 ≥ -56 / 7

⇔ x ≥ -8

S = [-8 ; +∞[

9x < 54

⇔ 9x / 9 < 54 / 9

⇔ x < 6

S = ]-∞ ; 6]

:-)

Answer:

10

Step-by-step explanation:

let the distance = d

d² = (x2-x1)² + (y2-y1)²

=>

10²= (x-4)²+(1+7)²

100 = (x-4)²+64

(x-4)²=100-64

= 36

x-4 = √36

x-4=6

x= 6+4

x= 10

Answer:

There are 360º in a circle. 140º has been allocated to one angle.

There are 360-140 = 220º left in the circle.

Step-by-step explanation:

Answer:

Mean speed = 41.3 mph

Step-by-step explanation:

Given that,

The speeds of an automobiles are given below:

20, 35, 42, 52, 65, 49, 24, 37, 23, 41, 50, 58

We need to find the mean speed of the cars.

Mean = sum of observations/ no. of observation

[tex]M=\dfrac{20+35+42+52+65+49+24+37+23+41+50+58}{12}\\\\M=41.3[/tex]

So, the mean speed of the cars is equal to 41.3 mph.

Answer:

The p-value of the test statistic from the standard normal table is 0.0017 which is less than the level of significance therefore, the null hypothesis would be rejected and it can be concluded that there is sufficient evidence to support the claim that less than 20% of the pumps are inaccurate.

Step-by-step explanation:

Here, 1304 gas pumps were not pumping accurately and 5689 pumps were accurate.

x = 1304, n = 1304 + 5689 = 6993

The level of significance = 0.01

The sample proportion of pump which is not pumping accurately can be calculated as,

The claim is that the industry representative less than 20% of the pumps are inaccurate.

The hypothesis can be constructed as:

H0: p = 0.20

H1: p < 0.20

The one-sample proportion Z test will be used.

The test statistic value can be obtained as:

[tex]Z=\frac{\hat{p}-P}{\sqrt{\frac{P(1-P))}{n}}}\\\\Z=\frac{0.186-0.20}{6993}\\\\Z=-2.927[/tex]

Answer:

It depends on what shape you have. Here are some formulas for different shapes.

Step-by-step explanation:

Rectangular prism: 2lw + 2lh + 2wh

Cylinder: 2 pi r² + 2 pi rh

Sphere: 4 pi r²

Cone: pi r² + pi rl

Square-based pyrimid: 1/2lp +B

I hope this helps!

Answer:

Time for a round trip = 12.5 hours

Step-by-step explanation:

Mother's house = 250 miles

Total distance for the round trip = 250 + 250 = 500 miles

Given speed = 40 mph

Find time .

[tex]Speed = \frac{distance }{Time }\\\\Time = \frac{distance }{speed } = \frac{500}{40} \\\\Time = 12.5 \ hours[/tex]

Answer:

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Answer:

Cost of adult ticket = $12.5

Cost of child ticket = $7.5

Step-by-step explanation:

Given:

Cost of 6 adult ticket and 5 child ticket = $112.5

Cost of 8 adult ticket and 4 child ticket = $130

Find:

Equation and solution

Computation:

Assume;

Cost of adult ticket = a

Cost of child ticket = b

So,

6a + 5b = 112.5....eq1

8a + 4b = 130 ......eq2

Eq2 x 1.25

10a + 5b = 162.5 .....eq3

eq3 - eq1

4a  = 50

Cost of adult ticket = $12.5

8a + 4b = 130

8(12.5) + 4b = 130

Cost of child ticket = $7.5

Answer:

3cm

use the formula for the volume of a cylinder

and substitute

Step-by-step explanation:

my answer is in the image above

Answer:

216 yd³

Step-by-step explanation:

Volume of a rectangular prism

= product of the three orthogonal sides

= 6yd * 6yd * 6yd

= 216 yd³

Answer:

216

Step-by-step explanation:

:)

Answer:

4-[tex]\frac{x}{2}[/tex]-[tex]x^{2}[/tex]

Step-by-step explanation:

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Red: 2

Blue: 4

Yellow: 4

[tex]\frac{2}{10}[/tex]

[tex]\frac{2/2}{10/2}=\frac{1}{5}[/tex]

Answer:

I'll setup the problem, then you can do the calculations

Step-by-step explanation:

Perimeter = 2width(W) + 2length (L)

Area = LW

L = 2.5 + 2W

LW = 62.5

substitute L in equation for area

[tex]2.5W + {2W}^{2} = 62.5 \\ \\ {2W}^{2} + 2.5 - 62.5 \\ \\ use \: quadratic \: solution \\\frac{ - b ± \sqrt{ {b}^{2} - 4ac}}{2a} [/tex]

a = 2; b = 2.5; c = 62.5

send a comment if you have a question

The perimeter of a rectangle.

P = 2 ( length + width )

The area of a rectangle.

Area = length x width

The perimeter of the rectangle shape garden bed is 32 feet.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

A rectangular shape Landscaper:

Width = W

Length = 2.5 + W

Area = 62.5 square feet

The perimeter of a rectangle.

P = 2 ( length + width )

The area of a rectangle.

Area = length x width

Now,

Area = 62.5

length x width = 62.5

(2.5 + W)  x W = 62.5

2.5W + W² = 62.5

W² + 2.5W = 62.5

W² + 2.5W - 62.5 = 0 ______(A)

The roots of this equation (A) are:

W = 6.75 and W = -9.25 (eliminated)

Now,

Length = 2.5 + 6.75 = 9.25 feet

Width = 6.75 feet

The perimeter of the rectangle.

P = 2 ( length + width )

P = 2 x (9.25 + 6.75)

P = 2 x 16

P = 32

Thus,

The perimeter of the rectangle shape garden bed is 32 feet.

Learn more about rectangles here:

https://brainly.com/question/15019502

#SPJ2

Answer:

120 pages

Step-by-step explanation:

The mean number of error per page = 8 ; Standard deviation = 1

Given that :

82 pages has between 7 and 9 errors per page ;

Using the empirical rule :

7 = 8 - 1 = 1 standard deviation below the mean

9 = 8 + 1 = 1 standard deviation above the mean

1 standard deviation from the mean = 68%

Hence, 82 pages = 68%

Approximate total pages :

68% = 82

100% = total pages, x

0.68 = 82

1 = x

0.68x = 82

x = 82 / 0.68

x = 120.588

Hence, total number of pages is 120 pages

Answer:

A,C,E

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

x/3x-1 divided by x-2/2x

= x/3x-1 * 2x/x-2

= 2x^2/(3x-1)(x-2).

If we expand the denominator it is

2x^2/(3x^2-7x+2).

Answer:

H0 : μ = 1220

H1 : μ > 1220

Test statistic = 1.30

Step-by-step explanation:

Sample mean, x = 1235.91

Standard deviation, σ = 211.67

Sample size, n = 300

The hypothesis :

Null ; H0 : μ = 1220

Alternative ; H1 : μ > 1220

Tbe test statistic :

(x - μ) ÷ (σ/√(n))

(1235.91 - 1220) ÷ (211.67/√(300))

15.91 / 12.220773

= 1.3018

= 1.30

Answer:

D. 56

Step-by-step explanation:

The general solution for the number of combinations with repetition is represented by the following expression:

[tex]x = \frac{(n + r - 1)!}{r!\cdot (n-1)!}[/tex] (1)

Where:

[tex]n[/tex] - Total number of elements.

[tex]r[/tex] - Number of the sample.

If we know that [tex]n = 6[/tex] and [tex]r = 3[/tex], then the number of combinations with repetition:

[tex]x = \frac{(6+3-1)!}{3!\cdot (6-1)!}[/tex]

[tex]x = 56[/tex]

Hence, correct answer is D.

Answer:

$84

Step-by-step explanation:

63÷3=21

63+21=84

Hope this helps! :)

Answer:

2/7

Step-by-step explanation:

Answer:

cant see it

Step-by-step explanation:

just type it out

Answer:

65%

Step-by-step explanation:

2080/3200times100%

The line integral is

[tex]\displaystyle \oint_C\mathbf F(x,y)\cdot\mathrm d\mathbf r = \int_0^2 \mathbf F(x(t),y(t))\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt \\\displaystyle= \int_0^2 (\sin^2(\pi t),-\cos^2(\pi t))\cdot(-\pi\sin(\pi t),\pi\cos(\pi t))\,\mathrm dt \\\displaystyle=-\pi\int_0^2(\sin^3(\pi t)+\cos^3(\pi t))\,\mathrm dt = \boxed{0}[/tex]

Answer:

a)89

b)89.45

Step-by-step explanation:

Answer:

The experiment shows the frequency of results derived from tossing a coin

Answer:

41

Step-by-step explanation:

substitute x=-2 and y=6, we know

8×6 +4×(-2) -(2×(-2) +3) = 48-8-(-1) =41

Answer:

41

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

8y + 4x - (2x + 3)

x = -2

y = 6

Step 2: Evaluate

Answer:

The restrictions for x would be 14 > x > 5.

Step-by-step explanation:

Let the length of the rectangle be y and the width be x.

That being said, the equation would be as follows:

[tex]y = 7x + 8[/tex]

[tex]y - 8 = 7x[/tex]

[tex]x = \frac{y-8}{7}[/tex]

Therefore, substituting the two values of y into the equations, we would get:

[tex]x = \frac{43-8}{7}[/tex]

[tex]x = \frac{35}{7}[/tex]

[tex]x = 5[/tex]

And:

[tex]x = \frac{106-8}{7}[/tex]

[tex]x = \frac{98}{7}[/tex]

[tex]x = 14[/tex]

Therefore, x would be between 5 and 14, and the restrictions for x would be 14 > x > 5.

Hope this helped!