Factor the trinomial below. x^2 + 5x – 24 A. (x – 8)(x + 3) B. (x – 4)(x + 6) C. (x – 3)(x + 8) D. (x – 6)(x + 4)

Answer:

The tree grows 33cm per year

Step-by-step explanation:

Here in this question, we are interested in knowing how fast the growth of the tree is.

This is easily obtainable from the equation for the height of the tree.

Mathematically, the equation is given as;

H = 210 + 33t

Interpreting this, we can have 210 as the original height of the tree when Renata moved in, while the term 33 represents the growth per year.

So we can say the tree adds a height of 33 cm each year and this translates to the yearly growth of the tree

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▹ Answer

6 phones

▹ Step-by-Step Explanation

$445 - $175 = $270

$270 ÷ $45 = 6

6 phones

Hope this helps!

CloutAnswers ❁

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Answer:

bde

Step-by-step explanation:

Answer:

B: The histogram shows there were 22 students in the class.

D: The histogram is symmetrical.

E:The histogram has a peak.

F: The histogram shows the data is evenly distributed.

Step-by-step explanation:

edg 2020

Step-by-step explanation:

Total catalysts = 10

Probability of 2 lower acidic catalysts = 2/10 = 1/5

Answer:

total amount paid = 32.5 + 28.9 + 24.95 = 86.35

20% of the total amount paid = 0.2 * 86.35 = 17.27

you tip 17.25$

Step-by-step explanation:

I(S) = aS / (S + c)

As S approaches infinity, S becomes much larger than c.  So S + c is approximately equal to just S.

lim(S→∞) I(S)

= lim(S→∞) aS / (S + c)

= lim(S→∞) aS / S

= lim(S→∞) a

= a

As S approaches infinity, I(S) approaches a.

Answer: 1023.75 (a)

Step-by-step explanation:

The sequence is a Geometric progression with the common ratio of ¹/₂ and first term of 512.

a = 512, r = ¹/₂. To determine the ratio, just divide the second term by the first term.

Now to calculate the sum, we consider two formula here and select the one that is most appropriate,

(1)  a( rⁿ - 1 )/r - 1, when r is greater than 1

(2) a( 1 - rⁿ )/1 - rⁿ, when r is less than 1.

In this question, formula 2 shall be appropriate because r is less than 1.

so,

S₁₂      =  512( 1 - 0.5¹² )/1 - 0.5

             512( 1 - 2.44 ₓ 10⁻⁴ )/0.5

          = 512( 0,9998 )/0.5

          = 511.875/0.5

          = 1023.75

The answer is a

Answer: 35 scoops total!

Step-by-step explanation: FIrst, you would add the number of scoops in total which is 3+1+1=5 scoops.

Now you would do 7*5=35

Therefore, Theo uses 35 scoops in all. I hope this helps you!

Answer:

Step-by-step explanation:

60°=2×30°

one angle is double the angle of the same right angled triangle.

so hypotenuse is double the smallest side.

Hypotenuse=10

smallest side=10/2=5

third side =√(10²-5²)=5√(2²-1)=5√3

Answer:

The answer is in the photo below. The interval is (-pi, pi) and the function is y = tanx.

We have

[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]

(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)

Recall for [tex]|x|<1[/tex], we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

So we have

[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]

Answer:

See answer and graph below

Step-by-step explanation:

∬Ry2x2+y2dA

=∫Ry.2x.2+y.2dA

=A(2y+4Ryx)+c

=∫Ry.2x.2+y.2dA

Integral of a constant ∫pdx=px

=(2x+2.2Ryx)A

=A(2y+4Ryx)

=A(2y+4Ryx)+c

The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2

The evaluation of the double integral is [tex]\mathbf{ \dfrac{105}{2}\pi }[/tex]

The double integral [tex]\mathbf{\int \int _R\ \dfrac{y^2}{x^2+y^2} \ dA}[/tex], where R is the region that lies between

the circles [tex]\mathbf{x^2 +y^2 = 16 \ and \ x^2 + y^2 = 121}[/tex].

Let consider x = rcosθ and y = rsinθ because x² + y² = r²;

Now, the double integral can be written in polar coordinates as:

[tex]\mathbf{\implies \int \int _R\ \dfrac{y^2}{x^2+y^2} \ dxdy}[/tex]

[tex]\mathbf{\implies \int \int _R\ \dfrac{r^2 \ sin^2 \theta}{r^2} \ rdrd\theta}[/tex]

[tex]\mathbf{\implies \int \int _R\ \ sin^2 \theta \ r \ drd\theta}[/tex]

Thus, the integral becomes:

[tex]\mathbf{=\int^{2 \pi}_{0} sin^2 \theta d\theta \int ^{11}_{4} rdr }[/tex]

∴

[tex]\mathbf{=\int^{2 \pi}_{0} \dfrac{1-cos 2 \theta }{2} \ \theta \ d\theta\dfrac{r}{2} \Big|^{11}_{4}dr }[/tex]  

[tex]\mathbf{\implies \dfrac{1}{2} \Big[\theta - \dfrac{sin \ 2 \theta}{2}\Big]^{2 \pi}_{0} \ \times\Big[ \dfrac{11^2-4^2}{2}\Big]}[/tex]

[tex]\mathbf{\implies \dfrac{\pi}{2} \times\Big[ 121-16\Big]}[/tex]

[tex]\mathbf{\implies \dfrac{105}{2}\pi }[/tex]

Learn more about double integral here:

https://brainly.com/question/19756166

Answer: Transitive property.

Step-by-step explanation:

First, for the equality we have:

Reflexive:

  For all real numbers x, x = x.

Symmetric:  

 For all real numbers x, y

 if x= y, then y = x.

Transitive:

 For reals x, y and z.

 if x = y, and y = z, then x = z.

Now, let's talk about inequalities.

first, the reflexive property will say that:

x > x.

This has no sense, so this property does not work for inequalities.

Now, the reflexive.

If x > y, then y > x.

Again, this has no sense, if x is larger than y, then we can never have that y is larger than x. This property does not work for inequalities.

Not, the transitive property.

if x > y, and y > z, then x > z.

This is true.

x is bigger than y, and y is bigger than z, then x should also be bigger than z.

x > y > z.

And this also works for the inverse case:

x < y and y < z, then x < z.

So the correct option is transitive property.

Answer: B. 25

Step-by-step explanation:

Given: Total books = 625

Number of books can fit in one box = 25

Now, the number of boxes she need to move all of the books = (Total books) ÷ (Number of books can fit in one box )

= 625÷25

= 25

hence, she requires 25 boxes in order to move all of the books.

So, correct option is B. 25.

Answer:

Step-by-step explanation:

From the given information;

let the hypotenuse be a , the opposite which is the north direction be b and the west direction which is the adjacent be c

SO, using the Pythagoras theorem

a² = c² + 177²

By taking the differentiation of both sides with respect to time t , we have

[tex]2a \dfrac{da}{dt} = 2c \dfrac{dc}{dt} + 0[/tex]

[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]

At c = 71 miles,[tex]a = \sqrt{ (71)^2 +(177)^2}[/tex]

[tex]a = \sqrt{ 5041+31329}[/tex]

[tex]a = \sqrt{ 36370}[/tex]

a = 190.71

SImilarly, [tex]\dfrac{dc}{dt} = \ 31 miles \ / hr[/tex]

Thus, the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles can be calculate as:

[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]

[tex]\dfrac{da}{dt} = \dfrac{71}{190.71} \times 31[/tex]

[tex]\dfrac{da}{dt} = 0.37229 \times 31[/tex]

[tex]\mathbf{\dfrac{da}{dt} = 11.54}[/tex]  to the nearest hundredth.

Answer:

The median would be 7.0.

Step-by-step explanation:

The median of a set of numbers means it is the middle number. since this set has 7 numbers you would need to find the number that is in the middle of the set. This would be the 4th number since it is in the middle. 7.0 is your answer.

Answer: 93-(18+30)=g

93-48=g

45=g

Step-by-step explanation: yup

The answer is 93-18-30-g=0 or 18+30+g=93

Answer:

For the null hypothesis to be rejected , then the conclusion of the test is that the absolute values of the z-statistic and/or the t-test statistic is greater than the critical value

Step-by-step explanation:

Here, we want to explain the conclusion of the test given that the null hypothesis is rejected.

Mathematically, the null hypothesis is as expressed as below;

H0: μ = 1,200

The alternative hypothesis H1 would be;

H1: μ > 1,200

Now, before we can reject or accept the null hypothesis, we will need a sample size and thus calculate the test statistics and the z statistics

For us to reject the null hypothesis, one of two things, or two things must have occurred.

The absolute value of the z statistic |z| or the test statistic |t| must be greater than the critical value.

If this happens, then we can make a rejection of the null hypothesis

[tex]\dfrac{5bc}{10b^2}=\dfrac{\not 5\cdot \not b\cdot c}{2\cdot \not 5\cdot \not b\cdot b}=\dfrac{c}{2b}[/tex]

Answer:

c / ( 2b)

Step-by-step explanation:

5bc/10b^2

Lets look at the numbers first

5/10 = 1/2

Then the variable b

b / b^2 = 1/b

Then the variable c

c/1 = c

Putting them back together

1/2 * 1/b * c/1

c/ 2b

Answer:

9 hours

Step-by-step explanation:

Since the group of men remains the same, number of hours is proportional to number of radios.

1300/26 = 450/h

h = 26 * 450 / 1300 = 9 hours

Answer:

-7/6

Step-by-step explanation:

-2/3 x 7/4 = -14/12 = -7/6

Answer: -7/6

Step-by-step explanation: (-2/3) ÷ (4/7) can be rewritten as (-2/3) · (7/4).

Remember that dividing by a fraction is the same thing

as multiplying by the reciprocal of the fraction.

Before multiplying however, notice that we

can cross-cancel the 2 and 4 to 1 and 2.

So multiplying across the numerators and denominator and

remembering our negative in the first fraction, we have -7/6.

Answer:

Option (B)

Step-by-step explanation:

The given expression is,

[tex]\sqrt{22x^6}\div\sqrt{11x^4}[/tex]

We can rewrite this expression as,

[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }[/tex]

Solving it further,

[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }=\frac{\sqrt{22(x^3)^2} }{\sqrt{11(x^2)^2} }[/tex] [Since [tex]x^3\times x^3=x^6[/tex] and [tex]x^{2}\times x^{2}=x^4[/tex]]

         [tex]=\sqrt{\frac{22(x^3)^2}{11(x^2)^2} }[/tex] [Since [tex]\frac{\sqrt{a} }{\sqrt{b} }=\sqrt{\frac{a}{b} }[/tex]]

         [tex]=\frac{x^3}{x^2}\sqrt{\frac{22}{11} }[/tex]

         [tex]=x\sqrt{2}[/tex]

Therefore, quotient will be x√2.

Option (B) will be the correct option.

Answer:

Step-by-step explanation:

Using the value for calculating the confidence interval as given;

CI = xbar + Z*σ/√n

xbar  is the mean = 37.14+42.86/2

xbar= 80/2

xbar = 40

Z is the z-score at the 90% confidence = 1.645

σ is the standard deviation

n is the sample size = 35

Given the confidence interval CI as [37.14, 42.86]

Using  the maximum value of the confidence interval to get the value of the standard deviation, we will have;

42.86 =  xbar + Z*σ/√n

42.86 = 40 + 1.645* σ/√35

42.86-40 = 1.645*σ/√35

2.86 = 1.645*σ/√35

2.86/1.645 = σ/√35

1.739 = σ/√35

1.739 = σ/5.92

σ= 1.739*5.92

σ = 10.295

Hence, the sample standard deviation of a pair of jeans is 10.295

Answer:

3 mL

Step-by-step explanation:

The fluid level is called the concave meniscus. The adhesive force causes it to crawl up on the sides, but you should ignore that while reading the level.

Answer:

30,455

Step-by-step explanation:

Exponential decay

y = a(1 - b)^x

y = final amount

a = initial amount

b = rate of decay

x = time

We are looking for the rate of decay, b.

900 = 450000(1 - b)^30

1 = 500(1 - b)^30

(1 - b)^30 = 0.002

1 - b = 0.002^(1/30)

1 - b = 0.81289

b = 0.1871

The equation for our case is

y = 450000(1 - 0.1871)^x

We are looking for the amount in 13 hours, so x = 13.

y = 450000(1 - 0.1871)^13

y = 30,455

Answer:

No, the owners are not having their transmissions serviced at 30,000 miles.

Step-by-step explanation:

We are given that a car dealer recommends that transmissions be serviced at 30,000 miles.

The car dealer selects a random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles.

Let [tex]\mu[/tex] = true average mileage of the automobiles serviced.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30,000 miles      {means that the owners are having their transmissions serviced at 30,000 miles}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 30,000 miles      {means that the owners are having their transmissions serviced at different than 30,000 miles}

The test statistics that will be used here is One-sample z-test statistics because we know about population standard deviation;

                             T.S.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~  N(0,1)

where, [tex]\bar X[/tex] = sample average mileage serviced = 30,456 miles  

            [tex]\sigma[/tex] = population standard deviation = 1684 miles

            n = sample of customers = 40

So, the test statistics =  [tex]\frac{30,456-30,000}{\frac{1684}{\sqrt{40} } }[/tex]  

                                     =  1.71

The value of z-statistics is 1.71.

Also, the P-value of the test statistics is given by;

                    P-value = P(Z > 1.71) = 1 - P(Z [tex]\leq[/tex] 1.71)

                                  = 1 - 0.9564 = 0.0436

For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.0436 = 0.0872.

Since the P-value of our test statistics is less than the level of significance as 0.0872 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that the owners are having their transmissions serviced at different than 30,000 miles.

Answer:

E(x)  [tex]= \frac{n+1}{2}[/tex]

Var(x) [tex]= \frac{1}{4} [ n - 1 ][/tex]

Step-by-step explanation:

Hint x = 1 + x1 + ......... Xn-1

[tex]X_{i} = \left \{ {{1} if the ith adjacent pair of magnets repel each other \atop {0} if ith adjacent pair of magnets join} \right.[/tex]

attached below is the detailed solutioN

usually like poles of magnets repel each other and unlike poles of magnets attract each other forming a block

Answer:

45

62x

______

  90

2700+

_________

2790

Step-by-step explanation:

Answer: 0.81

Step-by-step explanation:

[tex]81:19\ \text{can be written as the fraction}\ \dfrac{81}{81+19}=\dfrac{81}{100}=\large\boxed{0.81}[/tex]