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3 years ago

4x+10=x+5+50 What is the answer to this equation

Mathematics

2 answers:

goldenfox [79]3 years ago

5 0

Answer:

x=15

Step-by-step explanation:

4x+10=x+5+50

4x+10=x+55

4x-x+10=55

3x+10=55

3x=55-10

3x=45

x=45/3

x=15

xxMikexx [17]3 years ago

3 0

Answer:

x=15

Step-by-step explanation:

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Kyle divided his stamps

Marat540 [252]

Answer:

Step-by-step explanation:

Each page has 6 stamps. There are 3 pages. This is a simple multiplication problem, and so you do 3x6 to find the total number of stamps Kyle has. Thus, 3 times 6 is 18.

visual:

Page One: 6 stamps

Page Two: 6 stamps

Page Three: 6 stamps

6 + 6 + 6 = 18 (or just do 6x3)

6 0

2 years ago

What is the distance between the y-intercepts of the lines? Adding a picture please help

DerKrebs [107]

The equation of a line is:

y = mx + c

The m is the gradient of the line, and the c is the y-intercept of the line

That means that the y-intercept of [y = -4x + 3] is 3

and the y-intercept of [y = -4x + 4] is 4

So the distance between the two y-intercepts is:

4 - 3 = <u>1</u>

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3 years ago

A track-and-field athlete releases a javelin. The height of the javelin as a function of time is shown on the graph below. Use t

Georgia [21]

Part 1:

For this case we must see in the graph the axis of symmetry of the given parabola.
We have then that the axis of symmetry is the vertical line t = 2.
Answer:
The height of the javelin above the ground is symmetric about the line t = 2 seconds:

Part 2:

For this case, we must see the time t for which the javelin reaches a height of 20 feet for the first time.
We then have that when evaluating t = 1, the function is h (1) = 20. To do this, just look at the graph.
Then, we must observe the moment when it returns to be 20 feet above the ground.
For this, observing the graph we see that:
h (3) = 20 feet
Therefore, a height of 20 feet is again reached in 3 seconds.
Answer:
The javelin is 20 feet above the ground for the first time at t = 1 second and again at t = 3 seconds

5 0

3 years ago

The national mean annual salary for a school administrator is $90,00 a year (The Cincinnati Enquirer, April 7, 2012). A school o

timurjin [86]

Answer:

a) Null hypothesis: $\mu = 90000$

Alternative hypothesis: $\mu \neq 90000$

b) $p_v =2*P(t_{(24)}$

c) If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

Step-by-step explanation:

1) Data given and notation

77600 ,76000 ,90700 ,97200 ,90700 ,101800 ,78700 ,81300 ,84200 ,97600 ,

77500 ,75700 ,89400 ,84300 ,78700 ,84600 ,87700 ,103400 ,83800 ,101300

94700 ,69200 ,95400 ,61500 ,68800

We can calculate the sample mean and deviation with the following formulas:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

The values obtained are:

$\bar X=85272$ represent the mean annual salary for the sample

$s=11039.23$ represent the sample standard deviation for the sample

$n=25$ sample size

$\mu_o =90000$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Part a: State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean salary differs from 90000, the system of hypothesis would be:

Null hypothesis: $\mu = 90000$

Alternative hypothesis: $\mu \neq 90000$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Part b: Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{85272-90000}{\frac{11039.23}{\sqrt{25}}}=-2.141$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=25-1=24$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(24)}$

Part c: Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

6 0

3 years ago

Identify the volume of the composite figure rounded to the nearest tenth. HELP PLEASE!!

nirvana33 [79]

Answer:

V = 115.3 ft³

Step-by-step explanation:

The left part of the figure shows a cube of side length 4.2 ft. The volume of a cube is V = s³, where s is the side length. Hence, the volume of this particular cube is V = (4.2 ft)³ = 74.088.

The volume of a pyramid is V = (1/3)(base area)(height).

Here V = (1/3)(4.2 ft)²(7 ft) = 41.16 ft³.

Summing up the two distinct areas, we get V = 41.16 ft³ + 74.088 ft³, or

V = 115.3 ft³ after rounding up to the nearest tenth.

3 0

3 years ago