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3 years ago

15

Anthony writes a numerical expression 2+10x3-2 and says that the expression has a value of 34. Is Anthony correct? Explain your

answer.

1 answer:

lapo4ka [179]3 years ago

4 0

Answer:

Anthony is incorrect

According to the order of operations(PEMDAS), you must first multiply 10 × 3

which equals 30, then you add 2, which equals 32, finally you subtract 2, which brings you back to 30

10 × 3 = 30

2 + 30 - 2 = 30

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write an equation in point-slope form for the line that has a slope of 15 and contains the point (2,−9).

Lorico [155]

Answer:

y +9 = 15(x -2)

Step-by-step explanation:

The point-slope form of the equation for a line is ...

y -k = m(x -h) . . . . . . for slope m and point (h, k)

Here, you are given m=15 and (h, k) = (2, -9). Putting these values into the form gives the equation ...

y +9 = 15(x -2)

6 0

3 years ago

A hardware store receives a shipment of bolts that are supposed to be 12 cm long. The mean is indeed 12 cm, and the standard dev

Yuliya22 [10]

Answer: 0.9104

Step-by-step explanation:

Given : A hardware store receives a shipment of bolts that are supposed to be 12 cm long.

Mean : $\mu=12\text { cm}$

Standard deviation : $\sigma= 0.2\text{ cm}$

Sample size : n=10

Since, they will declare the shipment defective and return it to the manufacturer if the average length of the 100 bolts is less than 11.97 cm or greater than 12.04 cm.

So for the shipment to be satisfactory, the length of the bolts must be between 11.97 cm and 12.04 cm.

We assume that the length of the bolts are normally distributed.

Let X be the random variable that represents the length of randomly picked bolt .

For Z score : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x = 11.97

$z=\dfrac{11.97-12}{\dfrac{0.2}{\sqrt{100}}}=-1.5$

For x = 12.04

$z=\dfrac{12.04-12}{\dfrac{0.2}{\sqrt{100}}}=2$

By using the standard normal distribution table , the probability that the shipment is found satisfactory will be :-

$P(511.97$

Hence, the probability that the shipment is found satisfactory=0.9104

3 0

3 years ago

a number is equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller number and1. How ma

NeX [460]

Answer:

There is NO solution

Step-by-step explanation:

Considering 'y' be the number

Considering x be the smaller number

As 'y' is equal to twice a smaller number plus 3.

so

$y = 2x + 3$

also

y is equal to twice the sum of the smaller number and 1.

so

$y = 2x + 1$

so the system of equations become

$y = 2x + 3$

$y = 2x + 1$

solving

$\begin{bmatrix}y=2x+3\\ y=2x+1\end{bmatrix}$

$\mathrm{Subsititute\:}y=2x+1$

$\begin{bmatrix}2x+1=2x+3\end{bmatrix}$

$\mathrm{Refine\:}2x+1=2x+3$

$-2=0$

$-2=0\:\mathrm{\:is\:false,\:therefore\:the\:system\:of\:equations\:has\:no\:solution}$

$\mathrm{No\:Solution}$

Therefore, there is NO solution.

7 0

3 years ago

Adrian has a points card for a movie theater.

ANEK [815]

Answer: v ≥ 6

This means that Adrian needs to do at least 6 visits.

Step-by-step explanation:

First, we know that he gets 20 points just for signing up, so he starts with 20 points.

Now, if he makes v visits, knowing that he gets 2.5 points per visit, he will have a total of:

20 + 2.5*v

points.

And he needs to get at least 35 points, then the total number of points must be such that:

points ≥ 35

and we know that:

points = 20 + 2.5*v

then we have the inequality:

20 + 2.5*v ≥ 35

Now we can solve this for v, so we need to isolate v in one side of the equation:

2.5*v ≥ 35 - 20 = 15

2.5*v ≥ 15

v ≥ 15/2.5 = 6

v ≥ 6

So he needs to make at least 6 visits.

6 0

2 years ago

Integrate Sec (4x - 1) Tan (4x - 1) Dx

Delicious77 [7]

$\bf \displaystyle\int~sec(4x-1)tan(4x-1)dx \\\\[-0.35em] ~\dotfill\\\\ sec(4x-1)tan(4x-1)\implies \cfrac{1}{cos(4x-1)}\cdot \cfrac{sin(4x-1)}{cos(4x-1)}\implies \cfrac{sin(4x-1)}{cos^2(4x-1)} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int~\cfrac{sin(4x-1)}{cos^2(4x-1)}dx \\\\[-0.35em] ~\dotfill\\\\ u=cos(4x-1)\implies \cfrac{du}{dx}=-sin(4x-1)\cdot 4\implies \cfrac{du}{-4sin(4x-1)}=dx \\\\[-0.35em] ~\dotfill$

$\bf \displaystyle\int~\cfrac{~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{u^2}\cdot \cfrac{du}{-4~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{1}{4}\int\cfrac{1}{u^2}du\implies -\cfrac{1}{4}\int u^{-2}du \\\\\\ -\cfrac{1}{4}\cdot \cfrac{u^{-2+1}}{-1}\implies \cfrac{1}{4}\cdot u^{-1}\implies \cfrac{1}{4u}\implies \cfrac{1}{4cos(4x+1)}+C$

5 0

3 years ago