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3 years ago

Which is a solution of the equation 5(x-8) = -55

Mathematics

2 answers:

iogann1982 [59]3 years ago

8 0

Answer:

x = -3

Step-by-step explanation:

5(x-8) = -55

Divide each side by 5

5/5 (x-8) = -55/5

x-8 = -11

Add 8 to each side

x-8+8 = -11 +8

x = -3

Alexeev081 [22]3 years ago

7 0

Answer:

x= -3

Step-by-step explanation:

To solve the equation, we want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

5(x-8)= -55

x-8 is being multiplied by 5. The opposite of multiplication is division. Divide both sides by 5.

5(x-8)/5= -55/5

(x-8)= -55/5

(x-8)=-11

8 is being subtracted from x. The opposite of subtraction is addition. Add 8 to both sides.

x-8+8= -11+8

x= -11+8

x= -3

Let's check our solution. Plug -3 in for x in the original equation.

5(x-8)=-55

5(-3-8)= -55

5(-11)=-55

-55=-55

This is true, so we know that x is equal to -3.

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Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points betwee

julia-pushkina [17]

Answer:

89.04% of the data points will fall in the given range of z = − 1.6 and z = 1.6

Step-by-step explanation:

We are given a normally distributed data.

We have to find the percentage of data that lies within the range z = − 1.6 and z= 1.6

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

$P(-1.6 \leq z \leq 1.6)\\= P(z \leq 1.6) - P(z \leq -1.6)\\\text{Calculating the value from standard normal table}\\= 0.9452 - 0.0548 = 0.8904= 89.04\%$

89.04% of the data points will fall in the given range of z = − 1.6 and z= 1.6

6 0

3 years ago

After your yearly checkup, the doctor has some bad news and some good news. The bad news is that you tested positive for a serio

Maru [420]

Answer:

0.009804

Step-by-step explanation:

We are given;

probability of testing positive given that you have the disease is 0.99

Also, probability of not testing positive and not having the disease is 0.99

We are also told that it is a rare disease and so strikes only 1 in 1000 people = 0.0001

Let's denote positive test by T+, negative test by T¯, having the disease by D+, not having the disease by D¯.

So, we can now denote all the values in probability we have written earlier.

Thus:

P(T+ | D+) = 0.99

P(T¯ | D¯) = 0.99

P(D+) = 0.0001

Thus, P(D¯) = 1 - P(D+) = 1 - 0.0001 = 0.9999

Now, let's find probability of testing positive;

P(T+) = (P(T+ | D+) × P(D+)) + (P(T+ | D¯) × P(D¯))

Now, (P(T+ | D¯) is not given but by inspection, we can infer from the values given that it is 0.01

Thus;

P(T+) = (0.99 × 0.0001) + (0.01 × 0.9999)

P(T+) = 0.010098

Chances that one has the disease would be gotten from Baye's theorem;

P(D+ | T+) = (P(T+ | D+) × P(D+))/P(T+) = (0.99 × 0.0001)/0.010098 = 0.009804

7 0

4 years ago

Three consecutive even integers have a sum of 24. Find the integers

strojnjashka [21]

Even integers have the form 2k so three consecutive even integers will be 2k,2(k+1),2(k+2)
so there sum will be
2k+2(k+1)+2(k+2)=24
simplifying
2k+2k+2+2k+4=24
adding like terms
6k+6=24
6k=18
k=3
so the three consecutive even integers are
2(3),2(3+1),2(3+2)
6,8,10

5 0

3 years ago

Please help asap 100 points

vesna_86 [32]

Answers:

Problem #1: Option C, 166 yards cubed

Problem #2: Option A, 10

Step-by-step solution:

The first problem may seem a lot more confusing that it really is and this actually happened to me when I looked at it. Just because the cylinder is slanted that actually doesn't change any of the volume that we would have if it was straight up with the same diameter and height.

Using what we know about cylinders, let us plug all the information inside of the formula to determine the volume of the cylinder. However, before doing that we need to determine the radius of the circle from the diameter that was given.

Divide the diameter by two to get the radius

$Radius = \frac{Diameter}{2}$

$Radius = \frac{5.2\ yd}{2}$

$Radius = 2.6\ yd$

Plug in the values

$V_{cylinder} = (\pi * radius^2)*height$

$V_{cylinder} = (\pi * (2.6\ yd)^2)*7.8\ yd$

Simplify the exponent

$V_{cylinder} = (\pi * (2.6)^2 *(yd)^2)*7.8\ yd$

$V_{cylinder} = (\pi * 6.76\ yd^2)*7.8\ yd$

Simplify the expression

$V_{cylinder} = (21.237\ yd^2)*7.8\ yd$

$V_{cylinder} = 165.65\ yd^3$

Therefore, after simplifying the expression using the cylinder volume formula and the given information we were able to determine that the option that best fits the description of our answer is option C, 166 cube yards.

Now that we completed the first question, we can move onto the second question. In this question we are given a figure along with 3 numbers and one unknown, x, which we need to find the value of. We need to use the Secant-Secant Power Theorem to help determine our solution.

Make an expression to represent the scenario

$32(x + 32) = 28(20 + 28)$

We know have an expression which we can now simplify and get the value of the unknown easily. The first step would be to distribute the 32 and 28.

Distribute both sides

$32(x + 32) = 28(20 + 28)$

$(32 * x) + (32 * 32) = (28 * 20) + (28 * 28)$

$32x + 1024 = 560 + 784$

Simplify the expression

$32x + 1024 = 1344$

We now have a simple expression where we can now subtract both sides by 1024 to help isolate x with its coefficient.

Subtract 1024 from both sides

$32x + 1024 - 1024 = 1344 - 1024$

$32x = 1344 - 1024$

$32x = 320$

The final step that we have to help fully isolate x by itself is to divide both sides by 32 which would remove the coefficient from x.

Divide both sides by 32

$\frac{32x}{32} = \frac{320}{32}$

$x = \frac{320}{32}$

$x = 10$

After simplifying the expression completely, we are able to see that the best option that fits our description is option A, 10.

8 0

2 years ago

A deposit of $7,000 at 6.5% for 120 days. 151.67 358.97

astraxan [27]

120 days is approximately equals to 4 months. (30 days * 4 = 120 days)
Now you deposited 7000 dollars at 6.5% interests.
IN 1 months
=> 7000 * .065 = 455 dollars in 1 month is the interest
=> 455 * 4 months = 1820 dollars n 4 months
=> 7000 + 1820 = 8820 dollars.

3 0

4 years ago