Answer: Eli’s age is 24 years and Cora’s age is 74 years
Step-by-step explanation:
To find Eli’s age and Cora’s age, use the following condition.
Eli’s age is represented by term ‘x’
Cora’s age is represented by term ‘3x + 2’
x + 3x + 2 = 98
Add x and 3x
4x + 2 = 98
Subtract 2 from both sides
4x = 96
Divide by 4 on both sides
x = 24
Therefore Eli’s age is 24 years
To find Cora’s age, plug in 24 for x
3(24) + 2 = 72 + 2 = 74
Answer:
Cora is 74 years old
Eli is 24 years old
Step-by-step explanation:
Cora’s age = x
Eli’s age = y
x = 3y + 2
x + y = 98
x = 98 - y
98 - y = 3y + 2
98 - 2 = 3y + y
96 = 4y
24 = y
x + 24 = 98
x = 98 - 24
x = 74
What is the length of chord ML? 20 units 24 units 26 units 30 units
Answer: 24 units
Step-by-step explanation:
MO, NO and LO are radii.
If MO = 13, THEN LO = NO = 13
IF NO = 13 and NP = 8, THEREFORE,
PO = NO - NP
PO = 13 - 8 = 5
USING PYTHAGORAS, WE CAN FIND MP:
MP = Sqrt(MO^2 - PO^2)
MP = sqrt(13^2 - 5^2)
MP = sqrt(169 - 25)
MP = sqrt(144)
MP = 12 units
P is the midpoint of Segment ML,
THEREFORE,
MP = PL
ML = MP + PL
ML = 12 + 12
ML = 24 units
Answer: 24
Step-by-step explanation:
edge
In a recent year 5 out of 6 movies cost between $50 and $99 million to make. At this rate, how many movies in a year with 687 new releases would you predict to cost between $50 and $99 million to make
Answer:
573 movies
Step-by-step explanation:
Here, we have 5 out of 6 movies having that cost
Therefore the rate we will be working with is 5/6
Now there are 687 new releases, the value that cost the given price range will be; 5/6 * 687 = 572.5 which is approximately 573
Heidi runs 1/3 of a mile in 1/4 of an hour and Louis takes 1/2 of an hour to run 23 of a mile.Who has the faster running rate?
Answer:
As both Louis and Heidi runs at the same speed, both are running at equal speed of 1.33 miles per hour.
Step-by-step explanation:
We will calculate speed of both the person in miles per hour and then compare the speeds.
Speed = distance/time
_____________________________________
For Heidi
Distance = 1/3 miles
time = 1/4 hour
speed = 1/3 ÷ 1/4 = 4/3 miles per hour = 1.33 miles per hour
_______________________________________
For Louis
Distance = 2/3 miles (here it was given 23 miles but it appears to be 2/3 of a miles )
time = 1/2 hour
speed = 2/3 ÷ 1/2 = 4/3 miles per hour = 1.33 miles per hour
______________________________________________________
As both Louis and Heidi runs at the same speed, both are running at equal speed of 1.33 miles per hour.
Ten points! Solve for x: 1 x > 7 B) 4 x > 1 D) −2 < x < 1
[tex]\text{Solve:}\\\\1 < x + 3 < 4\\\\\text{Subtract 3 from all 3 sides}\\\\-2<x<1\\\\\boxed{-2<x<1}[/tex]
simplify √16n/m^3 1. 4√mn/n^2 2. 4√mn/m 3. √mn/4m 4. 4√mn/m^2
Answer:
4√mn/m^2
Step-by-step explanation:
√16n/m^3
= √16n/√m^3
= √4x4xn/√mxmxm
= 4√n/m√m
Rationalize by multiplying the numerator and the denominator by the denominator, which is a surd:
= (4√n x √m)/(m√m x √m)
= 4√mxn/m√mxm
= 4√mn/mxm
= 4√mn/m^2
NEED HELP NOWWW Which of the following is a monomial?
O A. 9/x
O B. 20x - 14
O C. 11 x^2
D. 20^9 - 7x
Answer: C
Step-by-step explanation:
A monomial is a expression where in it is x to the power of something, and x cannot be a denominator
a man buys a dozen cameras for $1800.He sells them at a profit of $36 each.Express his profit as a percentage of his selling price.
Step-by-step explanation:
The solution is the document i sent please check through.
plzzz help class 9 optional math
If tan theta =p show that sec theta*cosec theta =p+1/p
Answer:
[tex]sec(\theta) \times cosec(\theta) = \dfrac{tan^2 (\theta)+ 1}{tan (\theta)} = tan (\theta)+ \dfrac{1}{tan (\theta)} = p + \dfrac{1}{p}[/tex]
Step-by-step explanation:
The given trigonometric relations are
tan(θ) = p
sec(θ)×cosec(θ) = p + 1/p
We note that, when tan(θ) = p, we have;
p + 1/p = tan(θ) + 1/(tan(θ)) = (tan²(θ) + 1)/tan(θ)
By trigonometric ratios, we have;
tan²(θ) + 1 = sec²(θ) =1/cos²(θ) which gives;
(tan²(θ) + 1)/tan(θ) = 1/cos²(θ) × 1/tan(θ) = cos(θ)/sin(θ)×1/cos²(θ)
[tex]\dfrac{1}{cos^2(\theta)} \times \dfrac{cos (\theta)}{sin( \theta)} = \dfrac{1}{cos(\theta)} \times \dfrac{1}{sin( \theta)} = sec(\theta) \times cosec(\theta)[/tex]
Therefore;
[tex]If \ tan (\theta) = p \ then \ sec(\theta) \times cosec(\theta) = p + \dfrac{1}{p}[/tex]
A circle has a radius of 21 inches. What is the length of the arc intercepted by a central angle that measures 4π/7 radians? Express the answer in terms of π .
Answer:
12π inches
Step-by-step explanation:
s = rθ
s = (21) (4π/7)
s = 12π
The length of the arc will be;
⇒ Arc = 37.68 inches
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The central angle = 4π/7
And, A circle has a radius of 21 inches.
Now,
We know that in circle;
⇒ Arc = Radius × Angle
Substitute all the values, we get;
⇒ Arc = 21 × 4π/7
⇒ Arc = 3 × 4 × 3.14
⇒ Arc = 37.68 inches
Thus, The length of the arc will be;
⇒ Arc = 37.68 inches
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Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides
of this triangle?
O 5cm and 8 cm
O 6 cm and 7 cm
O 7 cm and 2 cm
8 cm and 9 cm
Answer:
Choice D - 8cm and 9cm.
Step-by-step explanation:
The other sides are not greater than 13.
A: 5 + 8 = 13
B: 6 + 7 = 13
C: 7 + 2 = 9
However, D is greater than 13 and is the correct answer.
D: 8 + 8 = 16.
Option d: 8 cm and 9 cm.
There is a theorem in mathematics stating:
" The sum of length of two sides of any triangle is greater than the rest third side"
According to that theorem, first three given options cant form the sides of the given triangle whose one side is 13 cm.
The 4th option has 8 cm and 9 cm for which we have:
8 + 9 > 13
Thus this option follows the theorem.
Hence fourth option is correct.
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The net of a solid is shown below:
Net of a square pyramid showing 4 triangles and the square base. The square base has side lengths of 3 inches. The height of each triangle attached to the square is 6 inches. The base of the triangle is the side of the square.
What is the surface area of the solid?
18 square inches
27 square inches
36 square inches
45 square inches
Answer:
The answer is 45 inches².
Step-by-step explanation:
First, you have to find the area of each triangle:
[tex]area = \frac{1}{2} \times base \times height[/tex]
[tex]let \: base = 3 \\ let \: height = 6[/tex]
[tex]area = \frac{1}{2} \times 3 \times 6[/tex]
[tex]area = \frac{1}{2} \times 18[/tex]
[tex]area = 9 \: \: {inches}^{2} [/tex]
Assuming that the formula for surface area of pyramid is Surface area = base area(area of square) × 4(area of triangle):
[tex]base \: area = 3 \times 3 = 9[/tex]
[tex]area \: of \: triangle = 9[/tex]
[tex]s.a = 9 + 4(9)[/tex]
[tex]s.a = 9 + 36[/tex]
[tex]s.a = 45 \: \: {inches}^{2} [/tex]
PLEASE HELP!! laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. find the probability that a randomly selected light bulb will last between 900 and 975 hours.
Answer:
P = 0.0215 = 2.15%
Step-by-step explanation:
First we need to convert the values of 900 and 975 to standard scores using the equation:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Where z is the standard value, x is the original value, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation. So we have that:
standard value of 900: [tex]z = \frac{900 - 750}{75} = 2[/tex]
standard value of 975: [tex]z = \frac{975 - 750}{75} = 3[/tex]
Now, we just need to look at the standard distribution table (z-table) for the values of z = 2 and z = 3:
z = 2 -> p_2 = 0.9772
z = 3 -> p_3 = 0.9987
We want the interval between 900 and 975 hours, so we need the interval between z = 2 and z = 3, so we just need to subtract their p-values:
P = p_3 - p_2 = 0.9987 - 0.9772 = 0.0215
So the probability is 0.0215 = 2.15%
Answer:
2.35 babyyyyyyyyyyy
Step-by-step explanation:
Acellus sux
how many cups in 34 gallons
Answer:
544 cups
Step-by-step explanation:
1 gallon consists of about 16.0047 cups, 34x16 is 544
if a mobile was sold for Rs.24408 after allowing 10% discount on the marked price and adding 13% VAT.Findthe discount amount.
Answer:
Hi, there!!!!
See explanation in pictures.
I hope it helps you...
Factorize: 14x^6-45x^3y^3-14y^6
Answer:
(7x^3+2y^3)(2x^3−7y^3)
Assume that the random variable X is normally distributed, with mean p = 100 and standard deviation o = 15. Compute the
probability P(X > 112).
Answer:
P(X > 112) = 0.21186.
Step-by-step explanation:
We are given that the random variable X is normally distributed, with mean [tex]\mu[/tex] = 100 and standard deviation [tex]\sigma[/tex] = 15.
Let X = a random variable
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 100
[tex]\sigma[/tex] = standard deviaton = 15
Now, the probability that the random variable X is greater than 112 is given by = P(X > 112)
P(X > 112) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{112-100}{15}[/tex] ) = P(Z > 0.80) = 1- P(Z [tex]\leq[/tex] 0.80)
= 1 - 0.78814 = 0.21186
The above probability is calculated by looking at the value of x = 0.80 in the z table which has an area of 0.78814.
What’s a possible value of an integer that is less than 14 units from 29 but no more than or equal to 18
Answer:
15, 16, 17, 18
Step-by-step explanation:
29-14=15
15, 16, 17, 18 are less than or equal to 18
What is the center of the circle with the equation (x+4)^2 + (y - 2)^2 = 16? a (-4, -2) b (4,2) c (-4, 2) d (4, -2)
Answer:
C) (-4, 2)
Step-by-step explanation:
Answer:
The center is ( -4,2) and the radius is 4
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
(x+4)^2 + (y - 2)^2 = 16
(x- -4)^2 + (y - 2)^2 = 4^2
The center is ( -4,2) and the radius is 4
How can 2182 be written as the sum of four consecutive whole numbers?
Answer:
544 + 545 + 546 + 547
explanation: if the numbers are consecutive whole numbers then it would be near the ¼ of the given number
Please answer this question now
Answer:
e =7.1
Step-by-step explanation:
[tex]Hypotenuse = 10\\Opposite =e\\Adjacent =7\\\\Using\:Pythagoras\:Theorem\\Hypotenuse^2=Opposite^2+Adjacent^2\\10^2 =e^2 + 7^2\\100 =e^2+49\\100-49=e^2\\\\51 =e^2\\\sqrt{51} =\sqrt{e^2}\\ e = 7.141\\\\e = 7.1[/tex]
Can someone help me with this question (:
I’d appreciate it!
brainliest to the correct answer/explanation) ♀️
Answer:
bet whats the question
Step-by-step explanation:
A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate. One plan is to select 400 voters, another plan is to select 1,600 voters. If the study were conducted repeatedly (selecting different samples of people each time), which one of the following would be true regarding the resulting sample proportions of "yes" responses?
A. Different sample proportions would result each time, but for sample size 400 they would be centered (have their mean) at the true population proportion, whereas for sample size 1,600 they would not.
B. Different sample proportions would result each time, but for sample size 1,600 they would be centered (have their mean) at the true population proportion, whereas for sample size 400 they would not.
C. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.
D. For either sample size, using the same size each time, as long as the samples are drawn with replacement, they would be centered (have a mean) at 0.
Answer:
C. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.
Step-by-step explanation:
From the given information;
A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate.
A random sample is usually an outcome of any experiment that cannot be predicted before the result.
SO;
One plan is to select 400 voters, another plan is to select 1,600 voters
If the study were conducted repeatedly (selecting different samples of people each time);
Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion. This is because a sample proportion deals with random experiments that cannot be predicted in advance and they are quite known to be centered about the population proportion.
Which is the graph of linear inequality 6x + 2y > -10?
Answer:
The top left one.
Step-by-step explanation:
Fix this into y intercept form: y=mx+b
y>-3x-5
Because y is greater than 3x-5, the shaded area should be positive, so the top right and the bottom right will be eliminated. Now, looking at the y intercept which is the 'b' in the equation, it is -5. So the y intercept on the graph should be on negative 5, which means that the top left one is the correct answer!
Hope this helped, BRAINLIEST would really help me:)
Option 1 is the correct choice.
We have a linear inequality -
6x + 2y > -10
We have to determine which of the following graphs depicts the inequality given above.
What is an Inequality?An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.
According to the question, we have -
6x + 2y > -10
Add - 6x on both sides of inequality, we get -
- 6x + 6x + 2y > - 10 - 6x
2y > - 6x - 10
Dividing both sides of the inequality by 2, we get -
y > - 3x - 5
Now, in order to plot the graph for this inequality, let -
y = - 3x - 5
Plot the line for the above equation. Remember to plot the graph in the form of dashed line since the inequality is strict inequality.
Consider the point (0, 0) -
Solve the inequality for the point (0, 0), we get -
0 > - 3 x 0 - 5
0 > - 5
Which is true.
Hence, shade the complete area on that side of line where the point
(0, 0) lies.
Therefore, Option 1 is the correct choice.
(Refer the image attached, for reference)
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im not sure wether to replace the minus signs with addition, so if you could help me that would be nice :) 1.2y+4.5-3.4y-6.3
Answer:
-2.2y - 1.8
Step-by-step explanation:
We are to simplify the expression:
1.2y + 4.5 - 3.4y - 6.3
Collect like terms:
1.2y - 3.4y + 4.5 - 6.3
Simplify:
-2.2y - 1.8
That is the answer.
Consider the y-intercepts of the functions:
f(x) = |x – 1] + 2
g(x) =
(x + 3)
h(x) = (x + 1) -3
1
What is the ordered pair location of the greatest y-intercept of the three functions?
Answer:
+3, 0
Step-by-step explanation:
y-intercept for f(x) is when x = 0, so it is +1, 0
y-intercept for g(x) is when x = 0, so it is +3, 0
y-intercept for h(x) is when x = 0, so it is -2, 0
The y-intercept of a function is the point where x = 0.
The ordered pair that represents the greatest y-intercept is (0,3)
The functions are given as:
[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]
[tex]\mathbf{g(x) = (x + 3)}[/tex]
[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]
Set x = 0, and solve the functions
[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]
Substitute 0 for x
[tex]\mathbf{f(0) = |0 - 1| + 2}[/tex]
[tex]\mathbf{f(0) = |- 1| + 2}[/tex]
Remove absolute brackets
[tex]\mathbf{f(0) = 1 + 2}[/tex]
[tex]\mathbf{f(0) = 3}[/tex]
[tex]\mathbf{g(x) = (x + 3)}[/tex]
Substitute 0 for x
[tex]\mathbf{g(0) = (0 + 3)}[/tex]
[tex]\mathbf{g(0) = 3}[/tex]
[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]
Substitute 0 for x
[tex]\mathbf{h(0) = (0 + 1) - 3}[/tex]
[tex]\mathbf{h(0) = 1 - 3}[/tex]
[tex]\mathbf{h(0) = - 2}[/tex]
Hence, the ordered pair that represents the greatest y-intercept is (0,3)
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students enter school in the morning through doors on opposite sides of cafeteria. At Ms. Logrieco's door,35 students enter in the first 10 minutes. At Mr. Riley's door,22 students enter in the first 8 mins. If students continue to arrive at school at the same rate,how many students do you expect to be in the cafeteria after 24 minutes?
Ms. Logrieco's door: 35 students per 10 minutes
Mr. Riley's door: 22 students per 8 minutes
Time Frame: 24 minutes
35 x 2 = 70
35 x 2/5 = 14
70 + 14 = 84
22 x 3 = 66
84 + 66 = 150
Thus, we can expect for 150 students to be in the cafeteria after 24 minutes.
Assume that adults have it scores that are normally distributed with a mean of 100 standard deviation of 15 find probability that randomly selected adult has an Iq between 89 and 111
Answer:
0.5346
Step-by-step explanation:
Find the z-scores.
z = (x − μ) / σ
z₁ = (89 − 100) / 15
z₁ = -0.73
z₂ = (111 − 100) / 15
z₂ = 0.73
Find the probability.
P(-0.73 < Z < 0.73)
= P(Z < 0.73) − P(Z < -0.73)
= 0.7673 − 0.2327
= 0.5346
Evaluate w+(-x)-2/3 where w= 5/9 and x=4/3
Answer:
-1/24
Step-by-step explanation:
Plug in X and W
5/8 - 4/3 - 2/3.
Combine like terms.
5/8 - 2/3.
Solve.
-1/24
Answer:
- 2 1/10
Step-by-step explanation:
In a survey conducted by the marketing agency 11mark, 241 of 1000 adults 19 years of age or older confessed to bringing and using their cell phone every trip to the bathroom (confessions included texting and answering phone calls).
(a) What is the sample in this study? What is the population of interest?
(b) What is the variable of interest in this study? ls it qualitative or quantitative?
(c) Based on the results of this survey, obtain a point estimate for the proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom.
(d) Explain why the point estimate found in part (c) is a statistic. Explain why it is a random variable. What is the source of variability in the random variable?
(e) Construct and interpret a 95% confidence interval for the population proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom.
(f) What ensures that the results of this study are representative of all adults 19 years of age or older?
Answer: kindly check explanation
Step-by-step explanation:
A) The sample is a fraction of the total population used in the study.
The sample is 1000 19 years of age or older U.S adult.
The population : all U.S adults aged 19 or older.
B.) Confession about bringing cell phone to the bathroom and it is a qualitative variable
C.) point estimate (p) :
Total number of sample = 1000
Number who confessed to bring cellphone = 241
p = 241/ 1000
= 241/1000 = 0.241
D.) The point estimate was deduced from the sample information and not the population. Random selection because selection is unbiased.
E.) 95% confidence interval (CI)
95% CI = (1 - 0.95) = 0.05
For a two-tailed test : 0.05 / 2 = 0.025
Z - score = 1.96
Error : (√[p(1 - p) / n])*z
1.96 * √0.241(1-0.241)/1000
1.96* √0.000182919
1.96 * 0.0135247
= 0.0265085
Boundary :
(0.241 - 0.0265085), (0.241 + 0.0265085)
(0.2144915, 0.2675085)
F) The sample can be said to be representative of the total population since the sampling was performed and participants were chosen at random.
Which statement about the function is true?
The function is positive for all real values of x where
x > –4.
The function is negative for all real values of x where
–6 < x < –2.
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.
Answer:
b
Step-by-step explanation:
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.