What is the factored form of the following expression?
25x2 + 70x + 49

Answer:

76

Step-by-step explanation:

Answer:

∠Q  = 53.13 degrees

Step-by-step explanation:

Given that ∆PQR, ∠P = 90degrees , this means that the triangle is a right angled triangle

Hence using the notation

SOH CAH TOA

where S is sine, C is cosine, T is tangent and O, A and H represents the size of the opposite, adjacent and hypotenuse sides

Considering  ∠Q and the given sides

PR=16cm is the opposite side,

PQ= 12 cm is the adjacent side hence we use TOA

Tan Q = 16/12 =

Q = Arc tan 16/12

= 53.13 degrees

Answer:

Hello!

Im using 3.14 for pi

circumference: 43.96

area: 153.86

Hope that helps!

Answer:

43.96km

Step-by-step explanation:

hope this helps, braniliest  plzz

Answer: 20.5

Step-by-step explanation:

The distance between the bottom of the ladder from the bottom of the building will be 20.5 feet.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

In the event that you place a 38-foot stepping stool against the highest point of a 32-foot building.

Let 'x' be the horizontal distance on the ground. Then the equation is given as,

38² = 32² + x²

Simplify the equation, then we have

1444 = 1024 + x²

x² = 420

x = 20.5 feet

The distance between the bottom of the ladder from the bottom of the building will be 20.5 feet.

More about the Pythagoras theorem link is given below.

https://brainly.com/question/343682

#SPJ2

Answer:

D. Yes, since the p-value of the one-sided test is less than 5%.

Step-by-step explanation:

Test if there is evidence that the proportion of large trucks carrying hazardous materials is less than 30%.

At the null hypothesis, we test that this proportion is of 30%, that is:

[tex]H_0: p = 0.3[/tex]

At the alternate hypothesis, we test if this proportion is less than 30%, that is:

[tex]H_1: p < 0.3[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.3 is tested at the null hypothesis:

This means that [tex]\mu = 0.3, \sigma = \sqrt{0.3*0.7}[/tex]

Of 350 randomly selected trucks, 87 were carrying hazardous materials.

This means that [tex]n = 350, X = \frac{87}{350} = 0.2486[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.2486 - 0.3}{\frac{\sqrt{0.3*0.7}}{\sqrt{350}}}[/tex]

[tex]z = -2.1[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.2486, which is the p-value of z = -2.1.

Looking at the z-table, z = -2.1 has a p-value of 0.0179.

The p-value of the test is 0.0179 < 0.05, which means that there is evidence at the 5% level that the proportion of large trucks carrying hazardous materials is less than 30%. Thus, the correct answer is given by option D.

Answer:

7/36

Step-by-step explanation:

Complete

A bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn. What is the probability of selecting a purple marble and then a white marble?

Total outcome = 2 + 7 = 9marbles

Pr(picking purple) = number of purple/total outcome

Pr(picking red) = 7/9

Since the first marble is not replaced, the total outcome becomes 8 marbles

Pr(picking white) = 2/8 = 1/4

Probability of selecting a purple marble and then a white marble = 7/9 * 1/4 = 7/36

Answer:30 boys

Step-by-step explanation: There are 120 students, three-fourths are girls. Nine out of twelve is equal to three fourths, if you add a zero to the end of twelve and nine you get 90 out of 120, which is how many girls there are. If you subtract 90 from 120 you get 30 or one-fourth. The number of boys is equal to one-fourth because there is only one-foutlrth left. So, there are 30 boys.

Answer:

A) -1

Step-by-step explanation:

anything raised to the zero power is 1 but if there is a negative without parentheses around it then it becomes -1

ex, (-4)° = 1

Answer:

It would be -1.

Step-by-step explanation:

This is because any postive number to the power of 0 equals 1 but since there is a negative sign, it would become -1.

Answer: i am sorry but the picture wont load-

Step-by-step explanation:

Answer:

Part A is 5/6 of the whole

Part B is 1/6 of the whole

Solution:

Assuming there are no other parts,

the Whole = A + B is the denominator:

Whole = 15 + 3 = 18

Part A = 15 and Part B = 3 are numerators for each fraction.

The fractions are then:

15/18 and 3/18

Meaning:

Part A is 15/18 of the whole

Part B is 3/18 of the whole

Reducing the fractions, it is also true that:

Part A = 5/6 of the whole

Part B = 1/6 of the whole

Step-by-step explanation:

i think it's linear equation

Answer:

b

Step-by-step explanation:

Answer:

1 [tex]\frac{2}{8}[/tex]

Step-by-step explanation:

The largest is 1 [tex]\frac{4}{8}[/tex], and the smallest is [tex]\frac{2}{8}[/tex]. 1 [tex]\frac{4}{8}[/tex] - [tex]\frac{2}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex].

Answer:

(-1, 1)

Step-by-step explanation:

Just look at where the two lines intersect and thats the soloution

Answer:

a) [tex]-225.000\,G[/tex], b) La cantidad de meses en los que el saldo fue inferior al permitido se calcula al dividir el descuento total por la multa mensual, c) El saldo fue menor durante 3 meses.

Step-by-step explanation:

a) Asumamos que la caja de ahorro es un recipiente, donde las entradas de dinero son positivas y las salidas negativas. Un descuento debe entenderse como negativa en tanto que se paga en función de no superar el saldo mínimo permitido en un período determinado. En consecuencia, el descuento sufrido por el padre de Leticia se describe como -225.000 G.

b) y c) La cantidad de meses en los que el saldo fue inferior al permitido se calcula al dividir el descuento total por la multa mensual, es decir:

[tex]x = \frac{225.000\,G}{75.000\,\frac{G}{mes} }[/tex]

[tex]x = 3\,meses[/tex]

Answer:

We accept H₀    p₁  =  p₂  : We don´t have evidence to support any difference between the proportions

Step-by-step explanation:

Information from Ivan Allen College;

Sample size  n₁  = 137

The proportion of students failing

p₁  =  0,283      q₁ =  1  -  p₁     q₁  =  1  -  0,283    q₁ =  0,717

Information from College of Computing:

Sample size   n₂  =  111

x₂  ( number of students failing )  =  22

The proportion of students failing

p₂  =  0,1981      q₂  =  1  -  0,1981     q₂  =  0,8019

Hypothesis Test:

Null Hypothesis:                             H₀          p₁  =  p₂

Alternative Hypothesis                  Hₐ          p₁  ≠  p₂

Alternative Hypothesis indicates the test is a two-tail test

Choosing a significance level   α  =  0,05   ( Confidence Interval 95%)

we get from z table   z(c)  = 1,64

To obtain z(s)

z(s)  =  (  p₁ -  p₂  ) / EED

EED = √(p₁*q₁)/n₁  +  p₂*q₂)/n₂

EED = √ (0,283*0,717)/137   +  ( 0,1981*0,8019)/111

EED = √  0,00148  +  0,00143

EED = 0,054

And

z(s)  = ( 0,283 -  0,1981 )/ 0,054

z(s) = 1,57

Comparing   z(c)  and  z(s)

z(c) > z(s)

Then z(s) is in the acceptance region for H₀ : We accept H₀

Answer:

$120,000,000

Step-by-step explanation:

Just do $123 million - $3 million

Answer:permutations

Step-by-step explanation:

Answer:

2x−12

Step-by-step explanation:

Answer:

2x−12

Step-by-step explanation:

Problem to solve:  

(x−6)2

Solve the product 2(x−6)

2x+2⋅−6

Multiply 22 times -6−6

2x-12

Final Answer

2x-12

2x−12

Answer:

8.

[tex]\sqrt[3]{\frac{7x^3}{64y^4} } = \frac{(7x^3)^{\frac{1}{3}} }{(64y^4)^{\frac{1}{3} }} =\frac{7^{\frac{1}{3} }*x}{4^3^{\frac{1}{3} }y^4^{\frac{1}{3} }} =\frac{x}{4} \sqrt[3]{\frac{7}{y^4} }[/tex]

9.

[tex]\frac{4+\sqrt{6} }{3\sqrt{6} } =\frac{(4+\sqrt{6} )(\sqrt{6}) }{3\sqrt{6} \sqrt{6} } =\frac{4\sqrt{6}+6 }{3*6} =\frac{4\sqrt{6} +6}{18} =\frac{2\sqrt{6} +3}{9}[/tex]

10.

[tex]\frac{2 + 5\sqrt{2} }{2-\sqrt{2} }= \frac{(2 + 5\sqrt{2})(2+\sqrt{2}) }{(2-\sqrt{2})(2+\sqrt{2} ) } = \frac{4+ 2\sqrt{2} + 10\sqrt{2} +10 }{2^2 -\sqrt{2}^{2} } =\frac{14 + 12\sqrt{2} }{4-2} =\frac{14 + 12\sqrt{2} }{2} = 7 + 6\sqrt{2}[/tex]

Answer:

b

Step-by-step explanation:

Answer:

a i think a

Step-by-step explanation:

Answer:

[tex]Area = 24\ in^2[/tex]

Step-by-step explanation:

Given

Let

[tex]a, b \to[/tex] opposite sides of each trapezoid

[tex]h \to[/tex] height

[tex]a = 2; \ \ \ b = 4 \ \ \ \ h = 2[/tex]

See attachment for trapezoids

Required

The combined area of the 4

First, we calculate the area of 1

[tex]Area = \frac{1}{2}(a + b) * h[/tex]

So:

[tex]A_1 = \frac{1}{2}(2 + 4) * 2[/tex]

[tex]A_1 = \frac{1}{2}*6 * 2[/tex]

Using a calculator

[tex]A_1 = 6[/tex]

The combined area is:

[tex]Area =n * A_1[/tex]

Where

[tex]n = 4[/tex] --- 4 blades

So:

[tex]Area = 4 * 6[/tex]

[tex]Area = 24\ in^2[/tex]

9514 1404 393

Answer:

  (a) 2 or 3

  (b) -13

Step-by-step explanation:

(a) A, B, and C are collinear if there is some constant 'c' such that ...

  B - A = c(C - A)

This will give rise to two equations in 'c' and 'k'.

  (k +1, k +4) -(0, 9) = c((2k, k+3) -(0, 9))

  (k +1, k -5) = c(2k, k -6)

And the two equations are ...

  k +1 = 2ck

  k -5 = c(k -6)

From the first, we find ...

  c = (k +1)/(2k)

From the second, we find ...

  c = (k -5)/(k -6)

Equating these expressions for c gives ...

  (k +1)/(2k) = (k -5)/(k -6)

  (k +1)(k -6) = 2k(k -5) . . . . . . . multiply by 2k(k-6)

  k^2 -5k -6 = 2k^2 -10k

  0 = k^2 -5k +6 = (k -3)(k -2)

Solutions that make the factors zero are ...

  k = 3  or  k = 2

There are two values of k that make the points collinear: 2 and 3.

__

(b) AB is parallel to CD when the slopes of the lines between them are the same

  slope of AB = (k+4 -9)/(k+1 -0) = (k -5)/(k +1)

  slope of CD = ((k +6 -(k +3))/(2k +2 -2k) = 3/2

Equating these slopes and solving for k, we get ...

  (k -5)/(k +1) = 3/2

  2(k -5) = 3(k +1)

  2k -10 = 3k +3

  -13 = k

AB is parallel to CD when k = -13.

_____

The attached shows the collinear points on the red and blue lines. The points that make parallel lines are shown on the purple lines. (The purple circles correspond to points D for k=2 and 3, so are irrelevant.) Point D is not labeled with its coordinates, (-24, -7).

Answer: - 2/3 but in decimal form it is -0.6 repeating

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

Answer:

$560

Step-by-step explanation:

In combinatorics, this question is a combination question, because combination deals with selection while permutations deal with arrangement.

[tex]nCr = \frac{n!}{(n - r)!r!} \\ [/tex]

Plugging in our values,

[tex]8C3 = \frac{8!}{(8 - 3)!3!} = \frac{8!}{5!3!} = \frac{8 \times 7 \times 6 \times 5!}{5!3!} = \frac{8 \times 7 \times 6}{3 \times 2} = 56 \\ [/tex]

That means 3 desserts from a tray of 8 desserts 56 times.