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Nadya [2.5K]
2 years ago
5

Find the integer values of x that satisfy both of these inequalities.

Mathematics
2 answers:
Ira Lisetskai [31]2 years ago
8 0

Answer:

x ∈ [-2/3, 3)

Step-by-step explanation:

5 − 3x ⩽ 7 and 4x + 1 < 13, this is given

-3x ≤ 7-5 and 4x < 13 -1, subtract 5 from first inequality and subtract -1 from second

-3x ≤ 2 and 4x < 12, combine like terms

x ≥ -2/3 and x < 12/4, divide by -3 and change the first inequality, and divide the second inequality by 4

x ≥ -2/3 and x < 3

[-2/3, ∞) and (-∞, 3)

x ∈ [-2/3, 3)

Shtirlitz [24]2 years ago
6 0

Answer:

0, 1, 2.

Step-by-step explanation:

5 - 3x <= 7

-3x <= 2

x >= -2/3      (the inequality sign flips as we are dividing by a negative value)

4x + 1 < 13

4x < 12

x < 3.

So the integer values satisfying the inequalities are>

0, 1, 2.

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1. Which of the following is not an equation?
OlgaM077 [116]

Answer:

2. is not an equation

Step-by-step explanation:

An equation always has an equal sign. An expression doesn't

5 0
2 years ago
Use the given information to answer the following questions. center (3, -9, 3), radius 5 (a) Find an equation of the sphere with
lianna [129]

Answer: The equation of the sphere with the center and radius

x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

Step-by-step explanation:

a) The equation of the sphere having center (h,k,l) and radius r is

(x-h)^{2} +(y-k)^2+(z-l)^2 = r^2

Given center of the sphere  (3, -9, 3) and radius 5

(x-3)^{2}+(y+9)^2+(z-3)^2 = 5^2

on simplification , we get solution

x^{2} -6 x+9+y^{2} +18 y+81+z^{2}-6 z+9=25

x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0

Final answer :-

x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

y^{2} +z^{2}+18 y-6 z+74=0

7 0
3 years ago
Does a statistics course improve a student's mathematics skills,as measured by a national test? Suppose a random sample of 13 st
viva [34]

Answer:

There is not enough evidence to support the claim that the scores after the stats course are significantly higher than the scores before (the difference in the scores is higher than 0).

P-value=0.042.

Step-by-step explanation:

The question is incomplete:

The data of the scores for each student is:

Before    After

430        465

485        475

520        535

360        410

440        425

500        505

425        450

470        480

515        520

430        430

450        460

495        500

540        530

We will generate a sample for the difference of scores (before - after) and test that sample.

The sample of the difference is [35 -10 15 50 -15 5 25 10 5 0 10 5 -10]

This sample, of size n=13, has a mean of 9.615 and a standard deviation of 18.423.

The claim is that the scores after the stats course are significantly higher than the scores before (the difference in the scores is higher than 0).

Then, the null and alternative hypothesis are:

H_0: \mu=0\\\\H_a:\mu> 0

The significance level is 0.01.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{18.423}{\sqrt{13}}=5.11

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{9.615-0}{5.11}=\dfrac{9.615}{5.11}=1.882

The degrees of freedom for this sample size are:

df=n-1=13-1=12

This test is a right-tailed test, with 12 degrees of freedom and t=1.882, so the P-value for this test is calculated as (using a t-table):

P-value=P(t>1.882)=0.042

As the P-value (0.042) is bigger than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the scores after the stats course are significantly higher than the scores before (the difference in the scores is higher than 0).

4 0
2 years ago
Convert 265 dm to feet. Round to 1 decimal
postnew [5]

Answer:

8.331 ft should be the answer if you're meaning centimeters!

8 0
2 years ago
2+2= need to kno thank you
netineya [11]

Answer:

Yay thanks for the free points I really! appreciate u!!

have a good day sir or ma'am. And 2+2 = 2+2

;-; :))

3 0
3 years ago
Read 2 more answers
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