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2 years ago

Which number(s) below belong to the solution set of the inequality? Check all that apply. 11x > 132

Mathematics

1 answer:

ozzi2 years ago

8 0

Answer:

Step-by-step explanation:

Note that

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

11x ≥ 132

divide both sides of the equation by 11

x ≥ 12

this means that the value of x is greater or equal to 12

In the option, the values that fit this condition are 12 and 26

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A deli sells ham for $2.98 per half pound. Kyle incorrectly says that the unit rate is $1.49 per pound. Explain Kyle's mistake a

sveticcg [70]

The correct answer per pound is $1.49 per pound. Kyle is correct because dividing 2.98/2= 1.49 or multiplying Kyle's answer by 2 will give you the correct amount!

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2 years ago

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The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of vi

baherus [9]

Answer: 2185

Step-by-step explanation:

Let p be the proportion of visitors are campers.

Given : The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of visitors who plan to camp in the state.

The prior proportion of visitors are campers : p=0.35

Allowable error : E= 2%= 0.02

We know that the z-value for 95% confidence = $z_c=1.96$

Then by Central Limit Theorem , the required sample size would be :

$n=p(1-p)(\dfrac{z_{c}}{E})^2$

$\Rightarrow\ n=0.35(1-0.35)(\dfrac{1.96}{0.02})^2\\\\ n= 0.35(0.65)(9604)$

Simply , we get

$n=2184.91\approx2185$ [Rounded to the next whole number.]

Hence, the smallest sample size to estimate the population proportion of campers =2185

7 0

2 years ago

The equation h(t) = -16t² + 80t + 64 represented the height, in feet, of a potato t seconds after it has been launched.

Lyrx [107]

Answer:

Part A) The potato hit the ground at t=5.70 seconds (see the explanation)

Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

we have

$h(t)=-16t^2+80t+64$

where

h(t) is the height of a potato in feet

t is the time in seconds

Part A) Write an equation that can be solved to find when the potato hits the ground. Then solve the equation

we know that

When the potato hit the ground, the value of h(t) must be equal to zero

For h(t)=0

$-16t^2+80t+64=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^2+80t+64=0$

$a=-16\\b=80\\c=64$

substitute in the formula

$t=\frac{-80\pm\sqrt{80^{2}-4(-16)(64)}} {2(-16)}$

$t=\frac{-80\pm\sqrt{10,496}} {-32}$

$t=\frac{-80+\sqrt{10,496}} {-32}=-0.70$

$t=\frac{-80-\sqrt{10,496}} {-32}=5.70$

therefore

The potato hit the ground at t=5.70 seconds

Part B) Write an equation that can be solved to find when the potato is 40 feet off the ground. Then solve the equation

For h(t)=40 ft

substitute in the quadratic equation

$-16t^2+80t+64=40$

$-16t^2+80t+24=0$

Solve the quadratic equation

we have

$a=-16\\b=80\\c=24$

substitute in the formula

$t=\frac{-80\pm\sqrt{80^{2}-4(-16)(24)}} {2(-16)}$

$t=\frac{-80\pm\sqrt{7,936}} {-32}$

$t=\frac{-80+\sqrt{7,936}} {-32}=-0.28$

$t=\frac{-80-\sqrt{7,936}} {-32}=5.28$

therefore

The potato is 40 feet off the ground at the time t=5.28 seconds

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2 years ago

Solve for x.<br> -15x + 60 ≤ 105 AND 14x + 11 ≤ -31

givi [52]

Answer:

x ≥ -3
x ≥ -3

Step-by-step explanation:

-15x + 60 ≤ 105

-15x ≤ 45

x ≥ -3

14x + 11 ≤ -31

14x ≤ -42

x ≥ -3

Best of Luck!

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2 years ago

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Generate a plan and describe the steps needed to solve the equation 34 (=-(m=3)????????

asambeis [7]

Answer:

-102x+34mx

Step-by-step explanation:

PLAN:

Distribute: $a\left(b+c\right)=ab+ac$ : 34x( - 3) + 34xm
Multiply and Simplify: -34 * 3x + 34mx
Multiply again: -102x + 34mx

<em>Hope this helps!!!</em>

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2 years ago

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Which number(s) below belong to the solution set of the inequality? Check all that apply. 11x > 132​

Which number(s) below belong to the solution set of the inequality? Check all that apply. 11x > 132