1. You roll two dice. What is the probability of rolling a sum of 8 or more?

4A.

antoniya [11.8K]

The number of paychecks Jalen will have to save until he can purchase the laptop is 6

<h3>How many paychecks will Jalen have to save until he can purchase the laptop? </h3>

Define your variable

To do this, we use the following variables

x represents the number of paychecks
y represents the cost of the laptop

Set up an equation, and solve it.

In (a), we have:

x represents the number of paychecks
y represents the cost of the laptop

Using the above variables, the equation is:

y = 200 + 50x

The cost of the laptop is $500.

So, we have:

200 + 50x = 500

Evaluate the like terms

50x = 300

Divide by 50

x = 6

Hence, the number of paychecks Jalen will have to save until he can purchase the laptop is 6

Read more about linear equations at:

brainly.com/question/14323743

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4 0

1 year ago

Suppose the total area is represented by the equation x^2+14x+24. If the area 1 is x^2 square units and area IV is 24 units, wha

Nutka1998 [239]

Answer:

See Explanation

Step-by-step explanation:

Given

$Total = x^2 + 14x + 24$

$Area\ I = x^2$

$Area\ IV = 24$

Required

True about area II and III

The question is incomplete; so, I will answer using general knowledge.

If the total area is:

$Total = x^2 + 14x + 24$

And there are 4 areas, then;

$Total = Area\ I + Area\ II + Area\ III + Area\ IV$

Rewrite as:

$Total = Area\ I + Area\ IV+ Area\ II + Area\ III$

This gives:

$x^2 + 14x + 24 = x^2 + 24+ Area\ II + Area\ III$

Collect like terms

$x^2 -x^2 + 14x + 24 -24= Area\ II + Area\ III$

$14x = Area\ II + Area\ III$

Rewrite as:

$Area\ II + Area\ III = 14x$

So, the sum of areas III and IV must be 14x

4 0

2 years ago

-4x – 2y=-12 4x + 8y=-24 Solve each system by elimination

kirza4 [7]

Answer:

x = 6 and y = - 6

Step-by-step explanation:

- 4 x - 2 y = -12.......equ No 1

4 x + 8y = - 24.......equ No 2

Adding equ No 1 and equ No 2

6 y = - 36

∴ y = - 6

substitute y = - 6 in equ No 2

4 x + 8 y = -24

4 x + 8 ×( -6) = - 24

4 x - 48 = -24

4 x = -24 + 48

4 x = 24

∴ x = 6

x = 6 and y = - 6

7 0

3 years ago

The work of a student to solve a set of equations is shown:

Alina [70]

In which step did the student first make an error?

Answer: Step 2

Step 2 should be:

−3y = -45 + 6z

7 0

3 years ago

Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean. See Attached Excel for Da

alexgriva [62]

Answer:

The 99% confidence interval for the mean germination time is (12.3, 19.3).

Step-by-step explanation:

The question is incomplete:

Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.

We start calculating the sample mean M and standard deviation s:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(18+12+20+17+14+15+13+11+21+17)\\\\\\M=\dfrac{158}{10}\\\\\\M=15.8\\\\\\$

$s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((18-15.8)^2+(12-15.8)^2+(20-15.8)^2+. . . +(17-15.8)^2)}\\\\\\s=\sqrt{\dfrac{101.6}{9}}\\\\\\s=\sqrt{11.3}=3.4\\\\\\$

We have to calculate a 99% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=15.8.

The sample size is N=10.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{10}}=\dfrac{3.4}{3.162}=1.075$

The degrees of freedom for this sample size are:

df=n-1=10-1=9

The t-value for a 99% confidence interval and 9 degrees of freedom is t=3.25.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=3.25 \cdot 1.075=3.49$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 15.8-3.49=12.3\\\\UL=M+t \cdot s_M = 15.8+3.49=19.3$

The 99% confidence interval for the mean germination time is (12.3, 19.3).

8 0

2 years ago