All categories

2 years ago

9. What four consecutive integers have a sum of -34?

Mathematics

1 answer:

givi [52]2 years ago

4 0

Given,

The four numbers are consecutive

The numbers are

x + 1

x + 2

x + 3

Sum = -34

x + (x + 1) + (x + 2) + (x + 3) = -34

x + x + 1 + x + 2 + x + 3 = -34

(x + x + x) + (1 + 2 + 3) = -34

3x + 6 = -34

3x = -34 - 6

3x = -40

x = -40/3

You might be interested in

⭐️ Does anyone know this?!

ladessa [460]

Vertical stretch by 2 units.

B

6 0

3 years ago

Greg needs to buy plastic spoons. Brand A has a box of 25 spoons for $1.99 . Brand B has a box of 42 spoons for $3.89 . Find the

Helga [31]

To find the price per spoon of brand A, divide the cost by the amount of spoons:

1.99 / 25 = 0.0796

Repeat this process for brand B:

3.89 / 42 = 0.0926

Brand A, at $0.08 a unit, is the better buy of brands A and B.

Hope this helps.

8 0

3 years ago

Read 2 more answers

Choose the correct reasoning of when a projectile reaches its highest point. A. A projectile reaches its highest point when its

alexira [117]

Answer: A projectile reaches its highest point when its vertical velocity component is zero.

Step-by-step explanation:

In projectile motion, objects moves in parabolic path.

Projectile motion is a type of motion in which an object moves in a bilaterally symmetrical, parabolic path. Projection motion happens when the force is applied at the start of the trajectory (where the object follows) which follows an interference which is gravity. Gravity takes over and afterwards the object accelerates downwards. The acceleration is constant so the vertical velocity (Vy) varies linearly. The maximum height of the projectile which is the highest height is reached when the vertical velocity (Vy) is equal to zero.

After the projectile reaches its maximum height which is its highest point, it begins to drop downwards.

5 0

2 years ago

The time to assemble the first unit on a production line is 8 hours. The learning rate is 0.81. Approximately how long will it t

pochemuha

Answer:

4.428 hours

Step-by-step explanation:

If the learning rate is 0.81, the slope of the learning curve is:

$b=\frac{ln(0.81)}{ln(2)} \\b=-0.304$

The time it takes to produce the n-th unit is:

$T_n=T_1*n^b$

If T1 = 8 hours, the time required to produce the seventh unit will be:

$T_n=8*7^{-0.304}\\T_n=4.428\ hours$

It will take roughly 4.428 hours.

3 0

3 years ago

Men are believed to have a slightly longer average length of short hospital stays than women; 5.2 days versus 4.5 days respectiv

Georgia [21]

Answer:

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of singificance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

Step-by-step explanation:

1) Data given and notation

$\bar X_{1}=5.2$ represent the mean for group men

$\bar X_{2}=4.5$ represent the mean for group women

Assuming these values for the remaining data:

$\sigma_{1}=1.2$ represent the population standard deviation for the sample men

$\sigma_{2}=1.5$ represent the population standard deviation for the sample women

$n_{1}=32$ sample size for the group men

$n_{2}=30$ sample size for the group women

z would represent the statistic (variable of interest)

$p_v$ represent the p value

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean for men it's higher than the mean for women, the system of hypothesis would be:

H0: $\mu_{1} \leq \mu_{2}$

H1: $\mu_{1} > \mu_{2}$

If we analyze the size for the samples both are higher than 30, and we know the population deviation's, so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

We have all in order to replace in formula (1) like this:

$z=\frac{5.2-4.5}{\sqrt{\frac{1.2^2}{32}+\frac{1.5^2}{30}}}=2.02$

4) Find the critical value

In order to find the critical value we need to take in count that we are conducting a right tailed test, so we are looking on the normal standard distribution a value that accumulats 0.01 of the area on the right and 0.99 of the area on the left. We can us excel or a table to find it, for example the code in Excel is:

"=NORM.INV(1-0.01,0,1)", and we got $z_{critical}=2.33$

5) Statistical decision

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of significance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

6 0

3 years ago