Answer:
x=2
Step-by-step explanation:
To solve, we need to isolate the variable, x
5x-18=2(3x-12) +4
Distribute the 2
5x-18=2*3x + 2*-12 +4
5x-18=6x-24+4
Combine like terms (add -24 and 4)
5x-18=6x-20
Add 18 to both sides
5x=6x-2
Subtract 6x from both sides
-x=-2
Divide both sides by -1
x=2
Answer: [tex]x=2[/tex]
Step-by-step explanation:
1. Get rid of the parenthesis. You can do this by multiplying.
[tex]5x-18=2(3x-12)+4[/tex]
[tex]5x-18=6x-24+4[/tex]
2. Move the variables to the left and the numbers to the right. If one of the numbers is not on its side (left or right) and you need to move it, change the sign.
[tex]5x-6x=-24+4+18[/tex]
Solve: Since the result is -1 and we have a variable, we can omit it.
[tex]-x=-24+22[/tex]
[tex]-x=-2[/tex]
Divide both sides by -1 to isolate the x
[tex]\frac{-(1)x}{-1} =\frac{-2}{-1}[/tex]
Solve:
[tex]x=2[/tex]
3. Proof: Replace the result in the original equation and both sides should be equal. (this step is for you to make sure that your answer is correct.
[tex]5x-18=2(3x-12)+4[/tex]
[tex]5(2)-18=2[3(2)-12]+4[/tex]
[tex]10-18=2(6-12)+4[/tex]
[tex]-8=2(-6)+4[/tex]
[tex]-8=-12+4[/tex]
[tex]-8=-8[/tex]
As you can see, both sides are equal to each other; which proves that [tex]x=2[/tex] is correct.
Logan is reading about architecture and learns that trusses can be used to support roofs. He wants to find the measures of the angles on a truss.The measure of ∠AFC is 120°, and the measure of ∠BFC is 95°. Which equation can you use to find the measure of ∠AFB?
The measure of ∠AFB is -35 degrees.
Explanation:To find the measure of ∠AFB, we can use the fact that the sum of the angles in a triangle is 180 degrees. Since we are given the measures of ∠AFC (120°) and ∠BFC (95°), we can find the measure of ∠AFB by subtracting the sum of these two angles from 180 degrees:
∠AFB = 180° - (120° + 95°) = 180° - 215° = -35°
Therefore, the measure of ∠AFB is -35 degrees.
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A company has developed a new battery, but the average lifetime of all of the batteries it makes is unknown. In order to estimate this average, a sample of 500 batteries is tested and the average lifetime of this sample is found to be 225 hours. The 225 hours is the value of a:
Answer:
The answer here would be Statistic.Step-by-step explanation:
In Statistics,Statistic is a term which refers to the values or estimates obtained from the sample to evaluate the actual population parameters.In this instance,observe that the average lifetime of the sample of 500 batteries tested comes out to be 225 hours., which is used to estimate the actual average lifetime of all the batteries developed by the company,which is also the population of interest in the concerned study.Hence,the average lifetime of the sample of 500 batteries of 225 hours is a sample Statistic which can be tested to determine the actual average lifetime of the all the batteries produced by the company.What is the least common multiple of 4 and 5?
Answer:
20
Step-by-step explanation:
Hi there,
To find the least common multiple (LCM) of 2 numbers, I would recommend listing off a few multiples of each number. Since they are small, it shouldn't be too hard.
Multiples of 4:
4, 8, 12, 16, 20
Multiples of 5:
5, 10, 15, 20
As you can see, the first multiple that 4 and 5 both share is 20. So the least common multiple of 4 and 5 20.
Solve the following: -3x(x-8)+7x=12
Step-by-step explanation:
Hello there!
Solve for x:
-3x(x-8)-7x=12
-3x^2+24x-7x=12
-3x^2+17x+12=0
Can you factor it further?Feel free to ask questions in the comments.
:)
Round 44.057 to the nearest hundredth.
Answer:
44.057 to nearest hundredth
44.06
In the derivation of the formula for the volume of a cone, the volume of the cone is calculated to be times the volume of the pyramid that it fits inside. Which expression represents the volume of the cone that is times the volume of the pyramid that it fits inside? (2r2h) (4r2h)
Answer:
D
Step-by-step explanation:
The formula to calculate the volume of the cone is π/4(1/3 x 4r²h).
The correct option is D.
What is a pyramid?A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.
Given:
In the derivation of the formula for the volume of a cone,
the volume of the cone is calculated to be π/4 times the volume of the pyramid that it fits inside.
The volume of the cone,
= π/4 (the volume of the pyramid)
= π/4 (1/3 x the base area x height)
= π/4(1/3 x 2r x 2r x h)
= π/4(1/3 x 4r²h)
Therefore, the volume is π/4(1/3 x 4r²h) cubic units.
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The complete question is given in the attached image.
The next two questions (Questions 7 and 8) refer to the following information: A Canadian study measuring depression level in teens (as reported in the Journal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). The researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis. If μ1 and μ2 represent the mean depression score for male teens and female teens respectively, which of the following is the appropriate pair of hypotheses in this case? (i) H0: μ1−μ2=0 Ha: μ1−μ2<0 (ii) H0: μ1−μ2>0 Ha: μ1−μ2=0 (iii) H0: μ1=μ2 Ha: μ1>μ2 (iv) H0: μ1−μ2=0 Ha: μ1−μ2>0 (v) Both (iii) and (iv) are correct.
Answer:
v- Both (iii) and (iv) are correct
Step-by-step explanation:
According to the Rule of Three, when we have a sample size n with xequals0 successes, we have 95% confidence that the true population proportion has an upper bound of StartFraction 3 Over n EndFraction . a. If n independent trials result in no successes, why can't we find confidence interval limits by using the methods described in this section? b. If 40 couples use a method of gender selection and each couple has a baby girl, what is the 95% upper bound for p, the proportion of all babies who are boys
Answer:
0 < p < 0.075
Step-by-step explanation:
Solution:-
According to the rule of three, when we have a sample size = n.
and x = 0 successes ( The lowest possible value of true population proportion ). Then we are 95% confident that the upper bound of the true population proportion is given by:
3 / n
If n = 40 couples use a method of gender selection and each couple has a baby girl, the the possibility of successes is zero. This calls on for the use of Rule of three to determine the upper bound for the true population of couple having a baby girl.
- The 95 % upper bound for true population proportion of all the babies born are girl is determined by:
p = 3 / n = 3 / 40
p ≈ 0.075
- The number of successes were = 0, hence the lower bound for the population proportion is 0 and the upper bound was calculated above. Hence,
0 < p < 0.075
- The range of true population proportion.
the proportion of all babies who are boys is 0 < p < 0.075
Calculation of the proportion:Here we know that the 95% confident that the upper bound of the true population proportion is provided by 3 by n
Since n be 40 couples
So, here the proportion should be
[tex]p = 3 \div n = 3 \div 40[/tex]
p ≈ 0.075
And, The number of successes were = 0
So, the proportion should be 0 < p < 0.075
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Identify the equivalent expression for each of the expressions below. Root(5, (m + 2) ^ 3). Root(3, (m + 2) ^ 5). Root(5, m ^ 3) + 2. Root(3, m ^ 5) + 2
Answer:
1. [tex](\sqrt[5]{(m+2)})^{3} = (m+2)^{\frac{3}{5}}[/tex]
2. [tex](\sqrt[3]{(m+2)})^{5} = (m+2)^{\frac{5}{3}}[/tex]
3. [tex]\sqrt[5]{(m)}^{3}+2 = m^{\frac{3}{5}}+2[/tex]
4. [tex]\sqrt[3]{(m)}^{5}+2 = m^{\frac{5}{3}}+2[/tex]
Step-by-step explanation:
Recall that
[tex](\sqrt[n]{x})^{m} = (x^{\frac{m}{n}})[/tex]
Where [tex]x^{m}[/tex] is called radicand and n is called index
1. Root(5, (m + 2) ^ 3)
In this case,
n is 5
m is 3
x = (m + 2)
[tex](\sqrt[5]{(m+2)})^{3} = (m+2)^{\frac{3}{5}}[/tex]
2. Root(3, (m + 2) ^ 5)
In this case,
n is 3
m is 5
x = (m + 2)
[tex](\sqrt[3]{(m+2)})^{5} = (m+2)^{\frac{5}{3}}[/tex]
3. Root(5, m ^ 3) + 2
In this case,
n is 5
m is 3
x = m
[tex]\sqrt[5]{(m)}^{3}+2 = m^{\frac{3}{5}}+2[/tex]
4. Root(3, m ^ 5) + 2
In this case,
n is 3
m is 5
x = m
[tex]\sqrt[3]{(m)}^{5}+2 = m^{\frac{5}{3}}+2[/tex]
The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1998.
Answer:
The projected world population in 1998 is 6,216,871,541.95
Step-by-step explanation:
Here we have the formula for exponential growth given by
A = P(1 + r)^t
Where:
A = Population at the end of the time period
P = Population at the start of the time period
r = Rate percent of population growth
t = Time period of interest
Therefore, given r = 2% = 2/100 = 0.02, P = 5,000,000,000;
t = year 1998 - year 1987 = 11 years
We have
A = 5,000,000,000 ×[tex](1+0.02)^{11}[/tex]= 6,216,871,541.95
≈ 6.2 billion.
To find the projected world population in 1998, we can use the exponential growth model. The initial population in 1987 was 5 billion with a growth rate of 2% per year. By applying the formula, the projected population in 1998 is estimated to be approximately 6.255 billion.
Explanation:To find the projected world population in 1998, we can use the exponential growth model. The formula for exponential growth is P = P0 * (1 + r)t, where P is the final population, P0 is the initial population, r is the growth rate, and t is the number of years.
In this case, the initial population (P0) in 1987 was 5 billion, the growth rate (r) was 2 percent per year, and we want to find the population in 1998, which is 11 years later.
Using the formula, we can calculate the projected population in 1998 as follows:
P = 5 billion * (1 + 0.02)11P = 5 billion * 1.0211P ≈ 5 billion * 1.251 = 6.255 billionTherefore, the projected world population in 1998 would be approximately 6.255 billion.
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One cubic foot of chemical weighs 80 pounds. How many pounds of the chemical can a container with the dimensions shown hold
To calculate how many pounds of a chemical a container can hold, you multiply the container's volume by the weight of the chemical per cubic foot. In the example given with a container measuring 4 ft x 3 ft x 2 ft, which has a volume of 24 cubic feet, the container would hold 1920 pounds of a chemical that weighs 80 pounds per cubic foot.
To answer your question on how many pounds of the chemical a container can hold, we need to calculate the volume of the container first and then use the provided density to find the weight of the chemical that fits in that volume. Unfortunately, the dimensions of the container are not provided in your question, so I'll give you an example of how to do this calculation instead.
Let's assume that the container is a box with the following dimensions: length (L) = 4 feet, width (W) = 3 feet, and height (H) = 2 feet. To find the volume (V) of the container, you multiply these dimensions:
V = L x W x H
V = 4 ft x 3 ft x 2 ft
V = 24 cubic feet
Now, to find out how much chemical can fit inside this volume, we use the fact that one cubic foot of the chemical weighs 80 pounds:
Weight of chemical in container = Volume of container x Weight per cubic foot
Weight of chemical in container = 24 cubic feet x 80 pounds/cubic foot
Weight of chemical in container = 1920 pounds
So, if the container had these assumed dimensions, it could hold 1920 pounds of the chemical.
Please I need the answer
Answer:
m and n a
Step-by-step explanation:
lines m and n are parallel .
Yasmin arrived home from play practice at 4:25 pm. The walk took 15 minutes. Practice began 20 minutes after the final bell and lasted for a half hour. When did school end
Answer:
3:20 pm.
Step-by-step explanation:
Time Yasmin got home: 4:25
Time it took to walk home: 15 minutes
Practice started: 20 minutes after bell.
Practice lasted for 30 minutes.
For us to find this out, you have to calculate all the activities.
An hour is 60 minutes.
A half hour is 30 minutes.
15 + 20 + 30 = 65 minutes.
65 minutes = an hour and five minutes.
4:25 - 1:05 = 3:20.
Feel free to let me know if you need more help! :)
Answer:
3:20 p.m
Step-by-step explanation:
At a restaurant, you decide to order the lunch special that includes one entree, one side and one drink. There are 6 entrees to choose from, 4 sides to choose from and 7 drinks to choose from. How many total options are there when ordering this meal
Answer:
168
Step-by-step explanation:
Total entree = 6
Total slides = 4
Total drinks = 7
Lunch special includes 1 entree, 1 slide, and one drink.
Option for entree
= 6_(c_1 )
= 6
Option for slides
= 4_(c_1 )
= 4
Option for drinks
= 7_(c_1 )
= 7
So, total option ordering meal,
= 6*4*7
= 168
7. What is the measure of ZE ?
Answer:
70 degrees
Step-by-step explanation:
The adjacent angles in a parallelogram are supplementary and add to 180 degrees
∠CDE+∠DEF=180
We know that ∠CDE is 110 degrees, so we can substitute that in
∠CDE+∠DEF=180
110+∠DEF=180
Subtract 110 from both sides
∠DEF= 70
So, ∠E is 70 degrees
What is the price of one crate of flowers?
Write the unit rate as a decimal in dollars and cents.
$
Answer:
$ 2.50
This is the right answer for ed2020
Answer:
$2.50
Step-by-step explanation:
Bc yeah <3
After 5 years, a $2,450 investment is worth $3,123.75.
What is the simple annual interest rate for this investment?
Answer:
5.5%
Step-by-step explanation:
To solve this problem we can use a modified version of the simple interest formula which is shown below:
[tex]r=\frac{I}{Pt}[/tex]
I = interest amount
P = principal amount
t = time (years)
The first step is to find the interest gained from the investment.
[tex]3,123.75-2,450=673.75[/tex]
Next, plug in the values into the equation:
[tex]r=\frac{673.75}{(2,450)(5)}[/tex] Multiply the bottom values
[tex]r=\frac{673.75}{12,550}[/tex] Divide the values
[tex]r=.055[/tex]
The last step is to convert 0.055 into a percent:
[tex]0.055(100)=5.5[/tex]
The interest rate is 5.5%
Two brothers are standing 3 feet away
from a mirror. How far away from
the brothers will their reflection
appear to be?
Answer:
3 feet
Step-by-step explanation:
Answer:
3 feet...
Step-by-step explanation:
Express the length of the kite string in terms of trigonometric ratios.
Answer:
[tex]\frac{70}{sin40^{\circ}}[/tex]
Step-by-step explanation:
We are given that
Height of the kite from the ground=h=70 feet
[tex]\theta=40^{\circ}[/tex]
We have to find the length of kite string in term of trigonometric ratios.
Let length of string=x
We know that
[tex]sin\theta=\frac{Perpendicular\;side}{hypotenuse}[/tex]
Using the formula
[tex]sin40^{\circ}=\frac{h}{x}[/tex]
[tex]sin40^{\circ}=\frac{70}{x}[/tex]
[tex]x=\frac{70}{sin40^{\circ}}[/tex]
Hence, the length of kite string=[tex]\frac{70}{sin40^{\circ}}[/tex]
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. According to a survey, the probability that an adult chosen at random is in favor of police body cameras is about 0.39.
Final answer:
The given statement exemplifies empirical probability because it is derived from the results of a survey, which is a real-life observation.
Explanation:
The statement 'According to a survey, the probability that an adult chosen at random is in favor of police body cameras is about 0.39' is an example of empirical probability.
Empirical probabilities are calculated from real-life observations or experiments. In this case, a survey is conducted, and the probability is calculated by dividing the number of adults in favor of police body cameras by the total number of adults surveyed. Since this probability comes from actual data collected from a population, it is empirical, as opposed to theoretical probability which is based on known mathematical principles or subjective probability which is based on personal judgment or opinion.
The statement is an example of empirical probability because it is based on data from a survey, reflecting observed frequencies in favor of police body cameras.
The given statement is an example of empirical probability. Empirical probability is based on observed data or past experiences.
In this case, the probability is determined through a survey, which involves collecting and analyzing data from a sample of adults.
The observed frequency of adults in favor of police body cameras is used to estimate the probability, making it empirical.
Which expression gives the best estimate of 30 percent of 61?
Answer:
c
Step-by-step explanation:
D I DID THE MATH
160% of 60 is how much?
please show step by step!
Answer:
96
Step-by-step explanation:
160% is the same as taking the number times 1.6
1.6 x 60 = 96
Debbie scored of her team's 24 points. How
many points did Debbie score?
Answer:
24
Step-by-step explanation:
Answer:
24 points
Step-by-step explanation:
An equation has solutions of m = -5 and m = 9. Which could be the equation?
(m + 5)(m - 9) = 0
(m - 5)(m + 9) = 0
m? - 5m + 9 = 0
m2 + 5m-9=0
Answer:
(m+5) (m-9) = 0
Step-by-step explanation:
An equation with solutions of m = –5 and m = 9 is y = m² − 4m − 45.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation.
Given that, the solutions of an equation are m = -5, and m = 9, we need to find the equation,
(m + 5) (m - 9) = 0
One possibility is that of a quadratic equation.
y = (m + 5) (m - 9)
y = m² - 9m + 5m - 45
y = m² - 4m - 45
Hence, an equation with solutions of m = –5 and m = 9 is y = m² − 4m − 45.
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Matias preformed an operation with 7.6 and a number. He ended up moving the decimal point in 7.6 two places to the left. Matias divided 7.6 by 10 raised to the power of
Answer:
Matias divided 7.6 by 10 raised to the power of -2.
Step-by-step explanation:
Given : Matias preformed an operation with 7.6 and a number. He ended up moving the decimal point in 7.6 two places to the left.
To find : Matias divided 7.6 by 10 raised to the power of ?
Solution :
Matias preformed an operation with 7.6 and a number.
He ended up moving the decimal point in 7.6 two places to the left we have to multiply it with 0.01
i.e. [tex]7.6\times 0.01=\frac{7.6}{100}=0.076[/tex]
So, Matias divided 7.6 by 10 raised to the power of -2.
Which point is on the circle centered at the origin with a radius of 5 units? Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
Answer:
Option A) [tex](2,\sqrt{21})[/tex]
Step-by-step explanation:
The following information is missing in the question:
A. [tex](2,\sqrt{21})[/tex]
B. [tex](2,\sqrt{23})[/tex]
C. (2, 1)
D. (2, 3)
We are given the following in the question:
A circle centered at origin and radius 5 units.
We have to find the equation of a point that lies on the circle.
Let (x,y) lie on the circle.
Distance formula:
[tex]d = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Putting
[tex](x_2,y_2) = (x,y)\\(x_1.y_1) = (0,0)\\d = 5[/tex]
We get,
[tex]5 = \sqrt{(y-0)^2 + (x-0)^2}\\\sqrt{x^2+y^2}=5\\x^2+y^2 = 25[/tex]
is the required equation of point on the circle centered at the origin with a radius of 5 units.
The point [tex](2,\sqrt{21})[/tex] satisfies the given equation.
Verification:
[tex](2)^2 + (\sqrt{21})^2\\=4 + 21\\=25[/tex]
Thus, [tex](2,\sqrt{21})[/tex] lies on the circle centered at the origin with a radius of 5 units.
Answer:
A. (2,\sqrt{21})
Step-by-step explanation:
A flagpole broke in a storm. It was originally 81 feet tall. 28 feet are still sticking straight out of the ground, where it snap, but the remaining piece has hinged over and touch the
Answer:
45ft
Step-by-step explanation:
The remaining piece has to be found. How far away is the end of the pole from the base of the pole along the ground.
We deduct original to broken 81-28 = 53 feet tall.
PT + to find the other side.
53^2 - 28^2 = S^2
√2025 = 45 = S^2
S^2 = 45ft
Which statement is true about point F? a.F is the midpoint of AA' because bisects AA'. b.F is the midpoint of EG because AA' bisects EG. c.F is the midpoint of AA' because AA' bisects EG. d.F is the midpoint of EG because bisects AA'.
Answer:
The correct option is;
a. F is the midpoint of [tex]\overline{AA'}[/tex] because line [tex]\overline{EG}[/tex] bisects [tex]\overline{AA'}[/tex]
Step-by-step explanation:
Here, since we have that the triangle is reflected across EG therefore the location of the point F which is along EG bisects the line [tex]\overline{AA'}[/tex] as the dimensions of the line from A to F must be equal to the dimension of the line that extends from A' to F
Therefore the point F is the midpoint of [tex]\overline{AA'}[/tex] because line [tex]\overline{EG}[/tex] bisects [tex]\overline{AA'}[/tex].
Answer:
A
Step-by-step explanation: i got it right on edge
I NEED THE ANSWER ASAP!! I WILL MARK BRAINLIEST!!
write a linear equation with the given information passing through point (-6,-1) and parallel to y=2x+1
Answer:
To find the line parallel to the line y = -2/3x + 1 and passing through the point (-6, -1), we will need to know that if two lines are parallel, then their slopes are equivalent to each other.
Since we are given the slope, we need to find the y-intercept of the line. We can find the y-intercept by substituting the point (-6, -1) into a new equation with the slope of m = -2/3. Remember that slope-intercept form is y = mx + b.
y = -2/3x + b (substitute the ordered pair)
-1 = -2/3(-6) + b
-1 = 4 + b (subtract 4 from both sides)
-5 = b
Therefore, the equation of the line passing through the point (-6, -1) and parallel to y = -2/3x + 1 is y = -2/3x - 5.
Step-by-step explanation:
I NEED THE ANSWER ASAP!! I WILL MARK BRAINLIEST!!
write a linear equation with the given information passing through
A large rainwater collection tub is shaped like a cylinder. The diameter is 28 inches and the height is 40 inches. If the tub is 75% filled, what is the volume of water in the tub? Round to the nearest tenth.
Answer:18472.6
use pie cylinder formula
Multiply the volume of the tub by 0.75 to find the volume of the water.
Step-by-step explanation:
To calculate the volume of water in the tub, you first find the radius of the cylinder, calculate the total volume, and then find 75% of that volume, finally converting the units if necessary and rounding to the nearest tenth, we get volume od water to be approximately 18451.2 cubic inches
To find the volume of water in the tub when it's 75% filled, we first need to find the volume of the entire tub and then multiply it by 75%.
The volume \ V of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- r is the radius of the cylinder,
- h is the height of the cylinder.
Given:
- Diameter d = 28 inches, so radius [tex]\( r = \frac{d}{2} = \frac{28}{2} = 14 \)[/tex] inches,
- Height h = 40 inches.
Substituting these values into the formula:
[tex]\[ V = \pi \times (14)^2 \times 40 \]\[ V = \pi \times 196 \times 40 \]\[ V = 7840\pi \, \text{cubic inches} \][/tex]
Now, to find the volume when the tub is 75% filled, we multiply the volume of the entire tub by 75% (or 0.75):
[tex]\[ \text{Volume of water} = 0.75 \times 7840\pi \, \text{cubic inches} \]\[ \text{Volume of water} = 5880\pi \, \text{cubic inches} \][/tex]
Now, let's compute the value:
[tex]\[ \text{Volume of water} \approx 5880 \times 3.14 \, \text{cubic inches} \]\[ \text{Volume of water} \approx 18451.2 \, \text{cubic inches} \][/tex]