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Answer:

x= -7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

-19x+32=-24x-3

-19x+24x=-3-32

5x=-35

X=-35/5= -7

Answer:

Last Option; 84 cu. mm

Step-by-step explanation:

We know that;

Volume = 1/3(Bh)

And that this is figure has a square base, therefore B that represents the area of the base will be: 6 * 6 = 36

And height = 7mm

Therefore we can say;

Volume = (1/3)*(6 x 6)*(7)

Volume = (1/3)*(36)*(7)

Volume = (12)*(7)

Volume = 84

Hope this helps!

Step-by-step explanation:

Perimeter of EFGH=2.5+1.5+4+2

=10

=

Answer:

D. Yes, because it passes the vertical line test

Step-by-step explanation:

Answer:

Perimeter = 9 . 4=36 ft

lateral area=(perimeter . slant height) / 2 = (36 . 12) /2 = 216 sq ft

area of the base=9*9=81 sq ft

Surface area = LA+BA = 216 + 81 = 297 sq ft

Answer:

Hence, the answer is [tex]x>71.1515[/tex]

Step-by-step explanation:

We have,

[tex]n=100,\mu=70,\sigma=7[/tex]

The top percentage of the students is [tex]5\%[/tex]

The  lower percentage of the students is [tex]95\%[/tex]

The lowest [tex]95\%[/tex] is the left area from the normal distribution table, the area [tex]0.95[/tex] lies in the z-table

[tex]z=1.645[/tex]       from the z- table

[tex]P(z<1.645)=0.95\\P(z>1.645)=0.05\\z>1.645[/tex]

[tex]\frac{x-\mu}{\frac{\sigma}{\sqrt{\mu}} } >1.645\\x>1.645\times \frac{\sigma}{\sqrt{n}} +\mu[/tex]

   [tex]>1.645\times \frac{7}{\sqrt{100}} +70[/tex]

   [tex]\Rightarrow x>71.1515[/tex]

Step-by-step explanation:

With the quadratic equation in this form: [tex]ax^2+bx+c=0[/tex]

Step 1: Find two numbers that multiply to give ac (in other words a times c), and add to give b.

Example: 2x^2 + 7x + 3

ac is 2×3 = 6 and b is 7

So we want two numbers that multiply together to make 6, and add up to 7

In fact 6 and 1 do that (6×1=6, and 6+1=7)

How do we find 6 and 1?

It helps to list the factors of ac=6, and then try adding some to get b=7.

Factors of 6 include 1, 2, 3 and 6.

1 and 6 add to 7, and 6×1=6.

Step 2: Rewrite the middle with those numbers:

Rewrite 7x with 6x and 1x:

2x^2 + 6x + x + 3

Step 3: Factor the first two and last two terms separately:

The first two terms 2x^2 + 6x factor into 2x(x+3)

The last two terms x+3 don't actually change in this case

So we get:

2x(x+3) + (x+3)

Step 4: If we've done this correctly, our two new terms should have a clearly visible common factor.

In this case we can see that (x+3) is common to both terms, so we can go:

Start with: 2x(x+3) + (x+3)

Which is: 2x(x+3) + 1(x+3)

And so: (2x+1)(x+3)

Done!

Check: (2x+1)(x+3) = 2x2 + 6x + x + 3 = 2x2 + 7x + 3 (Yes)

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Answer:

A

Step-by-step explanation:

Given p² varies inversely as q then the equation relating them is

p² = [tex]\frac{k}{q}[/tex] ← k is the constant of variation

To find use the condition when q = 6, p = 4 , then

4² = [tex]\frac{k}{6}[/tex]

16 = [tex]\frac{k}{6}[/tex] ( multiply both sides by 6 )

96 = k

p² = [tex]\frac{96}{q}[/tex] ← equation of variation

When p = 12 , then

12² = [tex]\frac{96}{q}[/tex] ( multiply both sides by q )

144q = 96 ( divide both sides by 144 )

q = [tex]\frac{96}{144}[/tex] = [tex]\frac{2}{3}[/tex] → A

Answer:

1 kg = 1000 grams

15,000 grams = 15kg

Answer:

parallelogram

Step-by-step explanation:

opposite sides are parallel and equal

The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units. So, all the options satisfy the value of a and b except (7, -9).

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly.

Then summing all those pieces' area gives us the area of the main big region.

The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units.

f(x) is a linear function, the area under the curve on the interval [0,4] is a trapezoid with a height of 4 and bases of lengths f(0) and f(4).

The area of a trapezoid is the height times the average of the bases.

a. f(x)=-2x+8  f(0)=8, f(4)=0;

   area = 4(8/2) = 16

b. f(x)=x+2; f(0)=2, f(4)=6;

   area = 4(8/2) = 16

c. f(x)=3x-2; f(0)=-2, f(4)=10;

    area = 4(8/2) = 16

d. f(x)=5x-6; f(0)=-6, f(4)=14;

    area = 4(8/2) = 16

e. f(x)=7x-9; f(0)=-9, f(4)=19;

     area = 4(10/2) = 20

Thus, The area is NOT 16 for choice e.

Learn more about Area here:

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Answer:

14

Step-by-step explanation:

Given

See attachment for proper stem plots for both district

Required

The sample size for Southeastern

The stem plot for southeastern is:

[tex]Stem | Leaf[/tex]

[tex]0 | 5\ 5\ 7\ 8[/tex]

[tex]1 | 1\ 2\ 3\ 5\ 9\ 9[/tex]

[tex]2 |2\ 7[/tex]

[tex]3 | 3[/tex]

[tex]4 | 1[/tex]

[tex]5 |[/tex]

To get the sample size, we simply count the leaves

The leaves are:

[tex]Leaves = \{5, 5, 7, 8, 1, 2, 3, 5, 9 ,9,2,7,3,1\}[/tex]

The number of leaves is:

[tex]n(Leaves) = 14[/tex]

Hence, the sample size is 14

Answer:

530!

Step-by-step explanation:

subtract the biggest value and the lowest value

Answer:

530

Step-by-step explanation:

Order the numbers from least to greatest, get the biggest and the lowest number and subtract both and then you find the range.

340,400,400,870

870-340= 530

Answer:

8422

Step-by-step explanation:

Answer:

Option 4, BC = 12.689, m∠A = 58°, and m∠C = 32°

Hope this helps!

Answer:

1.) 3833.8

2.) (3428.81 ; 4238.79)

Step-by-step explanation:

1.)

Point estimate of the salary for student with GPA of 3.

Using the regression model given :

Y = 2090.5 + 581.1x

x = 3

Y = 2090.5 + 581.1(3)

= 3833.8

2.)

95% confidence interval :

Y ± Tcritical * √MSE

Y = point estimate at x =3 ; = 3833.8

MSE = 21,284

Tcritical at 95% ; df = n-2 = 6-2 = 4

Tcritical(0.025 ; 4) = 2.776

√MSE = √21284 = 145.89036

Lower boundary : 3833.8 - 2.776(145.89036) = 3428.81

Upper boundary : 3833.8 + 2.776(145.89036) = 4238.79

(3428.81 ; 4238.79)

Answer:

c

Step-by-step explanation:

Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

So C would be the most accurate statement

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Answer:

H0: μ ≤ 1.30

H1: μ > 1.30

|Test statistic | > 1.833 ; Reject H0

Test statistic = 3.11

Yes

Pvalue = 0.006

Step-by-step explanation:

H0: μ ≤ 1.30

H1: μ > 1.30

Samples, X ; 1.36,1.35,1.33, 1.66, 1.58, 1.32, 1.38, 1.42, 1.90, 1.54

Xbar = 14.84 / 10 = 1.484

Standard deviation, s = 0.187 (calculator)

Decison rule :

|Test statistic | > TCritical ; reject H0

df = n - 1 = 10 - 1 = 9

Tcritical(0.05; 9) = 1.833

|Test statistic | > 1.833 ; Reject H0

Test statistic :

(xbar - μ) ÷ (s/√(n))

(1.484 - 1.30) ÷ (0.187/√(10))

0.184 / 0.0591345

Test statistic = 3.11

Since ;

|Test statistic | > TCritical ; We reject H0 and conclude that water consumption has increased

Pvalue estimate using the Pvalue calculator :

Pvalue = 0.006

Answer:

Step-by-step explanation:

Discussing interest starts with the principal, or amount your account starts with. This could be a starting investment, or the starting amount of a loan. Interest, in its most simple form, is calculated as a percent of the principal. For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5. The total amount you would repay would be $105, the original principal plus the interest.

Answer: A, C, D

Step-by-step explanation:

A is correct because Audrey reads 40 pages a day, and David reads 20. When you divide 40 by 20, you get 2. This means that 2 times 20 would be 40, and anything multiplied by 2 is "twice".

40 ÷ 20 = 2

2 × 20 = 40

B is not correct because after 6 days, Audrey reads 240 pages, and David reads only 120. We can figure this out by multiplying the pages read by 6.

Audrey: 40 × 6 = 240

David: 20 × 6 = 120

C is correct because when you subtract 20 from 40, you get 20. Since Audrey reads 40 pages a day and David reads 20, you can use this equation: 40-20 to figure the answer out. Audrey reads 20 more pages every day.

[tex]40-20=20[/tex]

D is correct because after 2 days, Audrey will have read 80 pages, and David will have read 40 pages. When you subtract 40 from 80, you get 40 pages.

40 × 2 = 80

20 × 2 = 40

80 - 40 = 40

E is not correct because, after 3 days, Audrey will have read 120 pages, and David will have read 60 pages. One-third of 120 is 40, not 60. Three times 60 would be 180, not 120. So, This answer is incorrect.

Answer:

Scalene,right angled triangle

Hope it helps

Answer: 37m

Step-by-step explanation:

Convert 300cm into m = 3m

6 + 6 + 3 + 3 + 3.5 + 3.5 + 12 = 37m

9514 1404 393

Answer:

  392 ft

Step-by-step explanation:

As in the attached figure, you seem to have sides b and c of the triangle, along with angle C. You want to find side 'a'. The law of sines can be used to find angle B, then angle A can be found from the sum of angles. Knowing angle A, we can find side 'a'.

  sin(B)/b = sin(C)/c

  sin(B) = (b/c)sin(C) = 400/550·sin(88°)

  B = arcsin(8/11·sin(88°)) ≈ 46.621°

Then angle A = ...

  A = 180° - B - C = 180° -46.621° -88° = 45.379°

Now, we can find side 'a' from ...

  a/sin(A) = c/sin(C)

  a = c·sin(A)/sin(C) ≈ 550·sin(45.379°)/sin(88°) ≈ 391.710 . . . feet

The unknown side of the triangle is about 392 feet.

Answer:

5. 2√6

6. 4

Step-by-step explanation:

5. x =√[3×(3+5] = √3×8 =√24=2√6

6. x(x+5)=6²

x²+5x=36

x²+5x-36=0

(x+9)(x-4) =0

x=-9 or x=4

Answer:

1/2, 2/4

Step-by-step explanation:

4/8 = (2/4) =1/2 (if you divide up and down by the same number)

so 4/8 = 1/2

next, let's simplify the choices we have:  (1/5) (2/6) (1/4) (1/2) (2/4)

1/5 is already simplified

2/6 = 1/3

1/4 is already simplified

1/2 is already simplified

2/4 = 1/2

Which of these is equal to 4/8 (aka 1/2)?

Answer: 1/2 and 2/4