Answers
The measure of ∡ PRQ, if the sum of an interior angle of a triangle is [tex]180^o[/tex] is 75°, so option B is correct.
What is the triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices.
Given:
The lines m and n are parallel,
∡ QPR = 70°
As the lines are parallel, the alternate angles will be equal,
∡PQR = ∡ QPN = 35°
The sum of the interior angles of the triangle is [tex]180^o[/tex]
∡ QPR + ∡ PRQ + ∡ RQP = 180
70 + 35 + ∡ PRQ = 180
∡ PRQ = 180 - 105
∡ PRQ = 75°
Therefore, the measure of ∡ PRQ, if the sum of an interior angle of a triangle is [tex]180^o[/tex] is 75°.
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Related Questions
Identify the following distribution as binomial, geometric or neither.
Draw a card from a standard deck of 52 playing cards, observe the card, and replace the card within the deck. Count the number of times you draw a card in this manner until you observe a jack.
a) Binomial.
b) Geometric.
c) Neither.
Answers
A 52-card standard deck of playing cards is drawn, examined, and then placed back into the deck is a geometric distribution.
Given that,
A 52-card standard deck of playing cards is drawn, examined, and then placed back into the deck.
We have to find count how many times a card is drawn in this way until a jack is seen.
We know that,
What is the geometric distribution?A discrete probability distribution known as a geometric distribution can be used to describe the likelihood of experiencing success for the first time following a string of failures. Up until the first success, a geometric distribution can undergo an infinite number of trials.
So,
P(X=x)=qˣp.
Therefore, A 52-card standard deck of playing cards is drawn, examined, and then placed back into the deck is a geometric distribution.
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Read the following prompt and type your response in the space provided.
Karen is writing a word problem that can be represented by the equation 2x + 3 = 13.
A bucket weights 2 grams and balls are put into it that each weight 3 grams. The total weight of the bucket and balls is 13 grams. How many balls are in the bucket?
Does her word problem fit the equation? Justify your response..
Answers
The equation has an x coefficient of 2. But the word problem has a x coefficient of 3 (balls are put into [the bucket] that each weigh 3 grams), where x, the unknown variable, is the number of balls.
Although the numbers are the same, Karen switched the 2 and 3 values when going from the equation to the problem.
Answer:can you copy and paste it?
Step-by-step explanation:
The domain of f(x,y) is the xy-plane, and values of f are given in the table below.
0 1 2 3 4
0 60 60 60 62 64
1 61 61 62 61 60
2 65 68 68 68 70
3 63 61 60 60 62
4 59 55 51 48 45
Find [tex]\int\limits_c grad f . dr[/tex] , where is
(a) A line from (0,1) to (1,2).
(b) A circle of radius 1 centered at (1,2) traversed counterclockwise.
Answers
Answer:
a) c[tex]\int\limits gradf.dr[/tex] = 1
b) c[tex]\int\limits gradf.dr[/tex] = 0
(the limit symbol has a circle in the center for part b)
Step-by-step explanation:
c[tex]\int\limits gradf.dr[/tex] = f(q) - f(p)
a) c[tex]\int\limits gradf.dr[/tex] = f(1, 2) - f(0, 1)
= 61 - 60
= 1
b) If C is the circle of radius 1 centered at the point beginning at point (1,2), we can think of C as both beginnings and ending at point ( 1, 3).
c[tex]\int\limits gradf.dr[/tex] = f(1, 3) - f(1, 3)
= 68 - 68
= 0
A bag contains 4 red marbles, 7 blue marbles and 8 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 10 th of a percent, that both marbles drawn will be green?
Answer=_____
Answers
The probability, to the nearest 10 th of a percent, that both marbles drawn will be green is 0.02
Given :
A bag contains 4 red marbles, 7 blue marbles and 8 green marbles. If two marbles are drawn out of the bag
Probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
total number of possible outcomes = 4 + 7 + 8
= 11 + 8
= 19
Total number of favourable outcomes = 7
probability = favourable outcomes / possible outcomes
= 7 / 19 * 18
= 7 / 342
= 0.02
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The Pacific halibut fishery has been modeled by the differential equation dy/dt= ky(1 - Y/M) where y(t) is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be M = 7 times 107 kg, and k = 0.78 per year. If y(0) = 2 times 107 kg, find the biomass a year later. (Round your answer to two decimal places.) times 107 kg How long will it take for the biomass to reach 4 times 107 kg? (Round your answer to two decimal places.) yr
Answers
The biomass a year later is [tex]& \ y \approx 3.23 \times 10^7 \mathrm{~kg}[/tex] and t=1.58 years to reach 4 times 107 kg of biomass.
The following differential equation: [tex]& \Rightarrow \frac{d y}{d t}=k y\left(1-\frac{y}{M}\right) \\[/tex]
[tex]& \Rightarrow \frac{d y}{d t}=k y\left(\frac{M-y}{M}\right)[/tex]
Using variable separable method:
[tex]$$\Rightarrow \frac{d y}{y(M-y)}=\left(\frac{k}{M}\right) d t$$[/tex]
Integrate both sides:
[tex]$$\begin{gathered}\Rightarrow-\int \frac{d y}{y(y-M)}=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int \frac{M}{y(y-M)} d y=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int \frac{y-(y-M)}{y(y-M)} d y=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int\left(\frac{1}{y-M}-\frac{1}{y}\right) d y=\int\left(\frac{k}{M}\right) d t\end{gathered}$$[/tex]
[tex]\Rightarrow-\frac{1}{M}(\ln (y-M)-\ln y)=\frac{k t}{M}+C \\[/tex]
Let C1 be a constant such that C1 = MC, therefore,
[tex]$$\begin{gathered}\Rightarrow-\ln (y-M)+\ln y=k t+C_1 \\\Rightarrow \ln \frac{y}{y-M}=k t+C_1 \\\Rightarrow \frac{y}{y-M}=e^{k t+C_1} \\\\\Rightarrow y=y e^{k t+C_1}-M e^{k t+C_1} \\\\\Rightarrow y e^{k t+C_1}-y=M e^{k t+C_1} \\\\\Rightarrow y=\frac{M e^{k t+C_1}}{e^{k t+C_1}-1} \\\\\Rightarrow y=\frac{M}{1-e^{-k t-C_1}} \\\Rightarrow y=\frac{M}{1-e^{-k t} e^{C_1}}\end{gathered}$$[/tex]
Let A be a new constant such that:
[tex]\Rightarrow y=\frac{M}{1-A e^{-k t}}[/tex]
Substitute the values of M and k, we'll get:
[tex]\Rightarrow y=\frac{7 \times 10^7}{1-A e^{-0.76 t}}[/tex]
Substituting the given initial condition:[tex]\Rightarrow y(0)=2 \times 10^7[/tex]
[tex]\Rightarrow 2 \times 10^7=\frac{7 \times 10^7}{1-A e^{-0.76(0)}} \\\\\\Rightarrow 2=\frac{7}{1-A} \\[/tex]
=2-2A=7
=A=-2.5
Therefore, [tex]\Rightarrow y=\frac{7 \times 10^7}{1+2.5 e^{-0.76 t}}[/tex]
On simplification, we'll get:
[tex]$$\begin{aligned}& \Rightarrow y \approx 32270466.08 \mathrm{~kg} \\& \Rightarrow y \approx 3.23 \times 10^7 \mathrm{~kg}\end{aligned}$$[/tex]
(b). Substitute the given value in the equation
[tex]$$\begin{gathered}\Rightarrow 4 \times 10^7=\frac{7 \times 10^7}{1+2.5 e^{-0.76 t}} \\\Rightarrow 4=\frac{7}{1+2.5 e^{-0.76 t}} \\\Rightarrow 4+10 e^{-0.76 t}=7\end{gathered}$$[/tex]
On simplification, we'll get t=1.58 years
Therefore, it will take for the biomass to reach 4 times 107 kg is 1.58 years.
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A hot air balloon rose at a constant rate. After 3 minutes, the balloon was 44 meters above
the ground. Then, 2 minutes later, the hot air balloon had risen to 70 meters above the
ground.
1A) How much did the hot air balloon rise each minute?
meters
___meters
1B) How far above the ground was the hot air balloon at the start of the ride?
___ meters
1C) Complete the equation that describes the relationship between the altitude of the hot air
balloon in meters, A, and the elapsed time in minutes, t.
Write your answer using whole numbers or decimals rounded to the nearest tenth.
A=___t+___
Answers
Make sure to give brainliest if this answer helps you!
1A) To find out how much the hot air balloon rose each minute, we need to find the rate at which it rose. The rate can be calculated by dividing the change in altitude by the change in time. In this case, the change in altitude is 70 meters - 44 meters = 26 meters, and the change in time is 2 minutes - 3 minutes = -1 minute (since the time is decreasing). The rate is therefore 26 meters/-1 minute = -26 meters/minute.
1B) The hot air balloon started at an altitude of 44 meters - (-26 meters/minute) * 3 minutes = 44 meters - (-78 meters) = 122 meters.
1C) To find the equation that describes the relationship between the altitude of the hot air balloon and the elapsed time, we can use the information that we have. The altitude at time t=0 is 122 meters, and the rate at which the altitude changes is -26 meters/minute. The equation is therefore A = -26t + 122.
The hot air balloon rise 13 m each minute.
The hot air balloon was 5 m above the ground at start.
The equation that describes the relationship between the altitude of the hot air balloon in meters is A = 13t + 5.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have, After 3 minutes, the balloon was 44 meters above the ground.
After 2 minutes later, the hot air balloon had risen to 70 meters above the ground.
1. The rate of change
= (70-44)/ (5-3)
= 26/ 2
= 13 m / min
2. At start the hot air balloon is
= (44-13 x 3)
= 5 m above the ground
3. The equation that describes the relationship between the altitude of the hot air balloon in meters is
A = 13t + 5.
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How is the quotient of 3,419 and 11 determined using an area model?
Answers
Answer:
37609
Step-by-step explanation:
You'd put the 3,419 inside the box and 11 outside the box.
But you'd need around 4 spaces inside the box for each number to be on top. And you'd need 2 spaces on the side. (Hopefully that makes sense)
Your answer should be 37609
If two lines are perpendicular, then the lines intersect to form four right angles that are 180º each.
True
False
Answers
Answer:
False. They would form 4 right angles (90)
Step-by-step explanation:
What expressions are equilvalent to 35+30s-45t?
Answers
Answer: 5(7+6s-9t)
Step-by-step explanation:
(note, this isn't the only expression that is equivalent but it's one of them)
You can notice that 35, 30, and 45 share a common factor of 5, and 5x7=35, 5x6=30, and 5x(-9)=-45, so:
5(7+6s-9t), which when you expand, it's equal to= 35+30s-45t
Write the equation in standard form. 4y−5x=3(4x−2y+1)
Answers
Answer:
To write the equation in standard form, we need to isolate the variables on one side of the equation and the constants on the other side. We can do this by combining like terms and using the distributive property.
First, we distribute the 3 on the right side of the equation:
4y - 5x = 12x - 6y + 3
Then, we combine like terms:
4y - 5x = 12x - 6y + 3
= -x + 6y + 3
Finally, we move all the constants to the right side of the equation and all the variables to the left side:
x - 6y = -3
This is the standard form of the equation. In standard form, the equation has the form ax + by = c, where a and b are coefficients, and c is a constant. In this case, the coefficients are 1 and -6, and the constant is -3.
Answer:
17x - 10y = - 3
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
4y - 5x = 3(4x - 2y + 1) ← distribute parenthesis
4y - 5x = 12x - 6y + 3 ( subtract 4y - 5x from both sides )
0 = 17x - 10y + 3 ( subtract 3 from both sides )
- 3 = 17x - 10y , that is
17x - 10y = - 3 ← in standard form
Solve:
b. m∠1=
m∠2=
m∠3=
Answers
The value of missing angles in the given figure are as follow:
m∠1= 56 ,m∠2= 56 and m∠3= 74.
As given in the question,
In the figure, MPQ is a triangle
We know that sum of the angles in the triangle is 180.
m∠ MPQ + m∠ PMQ + m∠1 =180
⇒58 + 66 + m∠1=180
⇒124 + m∠1= 180
⇒m∠1= 180 - 124
⇒m∠1=56
so m∠1=56.
∠1 and ∠2 are vertically opposite angles so ,
⇒m∠1= m∠2
therefore, m∠2=56.
Now in triangle QNO
∠QON + m∠2 + m∠3 =180
⇒50 + 56 +m∠ 3=180
⇒106 + m∠3= 180
⇒m∠3= 180 - 106
⇒m∠3=74
Therefore, the measure of the angles in the given figure are m∠1= 56 ,m∠2= 56 and m∠3= 74.
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Solve each equation.
Square root of x+x^2=0
Answers
The solutions to the equation √( x + x² ) = 0 are x = 0 and x = -1.
What is the solution(s) to the quadratic equation?Given equation in the question;
√( x + x² ) = 0
First, remove the radical of the left side of the equation by squaring both sides.
(√( x + x² ))² = 0²
x + x² = 0²
x + x² = 0
Next, factor the left side of the equation.
The common factor between x and x² is x
x( 1 + x ) = 0
Hence
x = 0
1 + x = 0
Subtract 1 from both sides
1 - 1 + x = 0 - 1
x = 0 - 1
x = -1
Therefore, the values of x are 0 and -1.
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consider a linear regression model where is a random vector with , , and no further assumptions are made about is an by deterministic matrix, and is invertible. is an unknown constant. let denote the least squares estimator of in this context. determine whether each of the the following statements is true or false. is the maximum likelihood estimator for .
Answers
False. The maximum likelihood estimator (MLE) is a method for estimating the parameters of a statistical model based on the maximization of the likelihood function. In the context of linear regression, the MLE would be the values of the parameters that maximize the likelihood of the observed data given the model.
The least squares estimator, on the other hand, is a method for estimating the parameters of a linear regression model by minimizing the sum of squared residuals, which is the difference between the observed response values and the fitted values predicted by the model. While the least squares estimator and the MLE can sometimes lead to similar estimates of the parameters, they are not the same thing and are derived using different principles.
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What is the product of any integer and -1?
Answers
Answer: Its the same number with the sign changed..
Step-by-step explanation:
5 multiplied by negative 1 would be -5
And
negative 5 multiplied by negative 1 would be 5
which of the following are calculated metrics for understanding analytical data? session and time on page entry and exit average session duration and page bounce rate revenue and revenue per session
Answers
From the provided topics to select, For the analytical data we need something where we can extract information from it. The answer is page bounce rate revenue and revenue per session.
What do you mean by data?In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.
What do you mean by analytical data?The systematic computational analysis of data or statistics is known as analytics. It is employed for the identification, explanation, and dissemination of significant data patterns. It also involves using data patterns to make smart decisions.
Page bounce rate revenue and revenue per session are the topics which contains some data and facts from which an analysis process can extract some information for other uses.
So, The metrics for understanding analytical data are page bounce rate revenue and revenue per session.
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Fran has a drawer containing 4 black T-shirts, 3. orange T-shirts, and 5 blue T-shirts. If she picks one T-shirt at random from the drawer, what are the chances that it will NOT be orange?
Answers
Answer: 75%
Step-by-step explanation: 4+3+5=12. 12-3=9. So the probability of not picking orange is 9/12, or 3/4. 3/4=75%. So the answer would be 75%
13) The pet shop has 6,157 dog treats. They packed the treats into bags with 7 pieces in each bag. Any treats
that did not fit into a bag of 7 were given to the groomer to use to reward animals getting bathed. How many
bags of treats did they fill? How many treats were given to the groomer?
bags of treats and gave
left over treats to the groomer.
Answer: The pet shop filled___bags of treats and gave ____left over treats to the groomer.
Answers
The number of bags filled by the pet shop is 879 and the number of treats they gave to the groomer is 4.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the data given in the question,
Total number of dog treats in the shop = 6157
Number of treats per bag = 7
Extra treats will be given to the groomer.
Then, the number of bags will be,
6157/7 = 879.57
This means that a total of 879 bags are there, with 7 pieces of treats per bag.
So, the total number of treats in 879 bags will be,
879 × 7 = 6153
So, the amount of treats left for the groomer is,
6157 - 6153 = 4 treats.
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Which equation of a line has a slope of -3 and passes through point (2, 4)?
y = 3x + 10
y = -3x + 10
y = 3x – 10
y = -3x – 10
Answers
Answer:
B
Step-by-step explanation:
y-4 = -3(x-2)
y - 4 = -3x + 6
y = -3x + 6 + 4
y = -3x + 10
Answer:
y = -3x+10
Step-by-step explanation:
Using the slope-intercept equation of a line
y = mx+b where m is the slope and b is the y intercept
y = -3x+b
Substitute the point into the equation
4 = -3(2) +b
4 = -6+b
10 =b
y = -3x+10
Give the POINT SLOPE equation of the line
that contains:
f(-1) = -7 and f(3) = -6.
Answers
This is one way we can represent a linear equation:
[tex]y-y_1=m(x-x_1)[/tex]
[tex](x_1,y_1)[/tex] is a point that falls on the line[tex]m[/tex] is the slopeSolving the QuestionWe're given:
Line contains [tex]f(-1) = -7[/tex] and [tex]f(3) = -6[/tex]These functions give us information on two points, as they are represented as [tex]f(x)=y[/tex]:
[tex]f(-1) = -7[/tex] ⇒ (-1, -7)[tex]f(3) = -6[/tex] ⇒ (3,-6)First, solve for the slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
⇒ Plug in the two points:
[tex]m=\dfrac{-6-(-7)}{3-(-1)}\\\\m=\dfrac{-6+7}{3+1}\\\\m=\dfrac{1}{4}[/tex]
⇒ Plug this into [tex]y_2-y_1=m(x_2-x_1)[/tex]:
[tex]y-y_1=\dfrac{1}{4}(x-x_1)[/tex]
Now, there are two ways we can write this equation, as we are given two points:
(-1, -7)
⇒ [tex]y-(-7)=\dfrac{1}{4}(x-(-1))\\y+7=\dfrac{1}{4}(x+1)[/tex]
(3,-6)
⇒ [tex]y-(-6)=\dfrac{1}{4}(x-(3))\\y+6=\dfrac{1}{4}(x-3)[/tex]
Answer[tex]y+7=\dfrac{1}{4}(x+1)[/tex] or [tex]y+6=\dfrac{1}{4}(x-3)[/tex]
Rick deposits $3 into his bank account. The following week, he deposits 3 times that amount. Each week after that, he deposits 3 times the amount he did the previous week. How much does he deposit in all during the first 3 weeks?
Answers
Answer:
answer on the picture......
a clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. in particular, historical data shows that 6000 shirts can be sold at a price of $55, while 8000 shirts can be sold at a price of $47. give a linear equation in the form p
Answers
So a linear equation in the form p is P(n) = -$0.004*n + $79.
We have two data points:
6000 shirts can be sold for $55 each.
8000 shirts can be sold for $47 each.
Then we can define the relation:P(n).
Where P is the price, and n is the number of shirts.
Now, we know that we can model this as a linear relationship that passes through the points (6000, $55) and (8000, $47)
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case, the slope is:
a = ($47 - $55)/(8000 - 6000) = -$0.004
Then our equation is:
P(n) = -$0.004*n + b
Now let's find the value of b, we know that:
P(6000) = $55= -$0.004*6000 + b
$55 = -$24 + b
b= $79
Our equation is:
P(n) = -$0.004*n + $79.
The linear equation P(n) = -$0.004*n + $79 has the form p.
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Statement
Reason
The coordinates of point D are (4, 5) and coordinates of point E are (5, 3) By the midpoint formula
Length of segment DE is √5 and length of segment AC is 2√5
Segment DE is half the length of segment AC
Slope of segment DE is -2 and slope of segment AC is -2
Segment DE is parallel to segment AC
Which of the following completes the proof? (6 points)
By the addition property
O By the distance formula
By construction
Given
By substitution
By the slope formula
Slopes of parallel lines are equal
Answers
By the slope formula, it is proved that the slope of AC is the same as the slope of DE thus option (D) is correct.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
As per the given,
D(4,5) and E(5,3)
Slope = (3 - 5)/(5 - 4) = -2
A(6,8) and C(8,4)
Slope = (4 - 8)/(8 - 6) = -4/2 = -2
Since the slope of DE = slope of AC
Therefore, both lines will be parallel by the slope formula.
Hence "It is established using the slope formula that the slopes of AC and DE are the same".
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The complete diagram is below,
To accumulate $10,000 at the end of 3n years, deposits of $86 are made at the end of each of the first 2n years and 98 at the end of each of the next n years. The effective annual rate of interest is i. You are given (1+i)^n = 2.0. Determine i.
Answers
If you want to have $10,000 at the end of 3n years, you must deposit $86 at the end of the first 2n years and $98 at the end of each subsequent n years (12.25%).
How is the annual interest rate determined?Effective yearly interest rate is equal to (1 + (nominal rate divided by the number of compounding periods)). (Amount of compounding intervals) minus 1.
This would be: 10.47% = (1 + 10% x 12) x 12 - 1 for investment A.
It would be as follows for investment B: 10.36% = (1 + (10.1% 2)) 2 - 1.
The annual interest rate is it monthly or yearly?The interest payment that the borrower pays the lender is determined by the interest rate. Lenders' quoted interest rates are yearly rates. The interest payment on the majority of house mortgages is computed monthly. As a result, the rate is divided by 12 before the payment is determined.
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Skylar and Wyatt both play soccer. Wyatt scored 2 times as many goals as Skylar. Together, they scored 15 goals. Could Skyler have scored 3 goals? Why or why not?
No, because 3(2) + 3 ≠ 15
No, because 3(2) ≠ 15
Yes, because 3 goals is less than the total number of goals scored
Yes, because 3 goals is less than the number of goals Wyatt scored
Answers
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Answer:
The correct answer is A. No, because 3(2) + 3 ≠ 15.
Step-by-step explanation:
because the total number of goals scored by Skylar and Wyatt was 15, and if Skylar scored 3 goals, then Wyatt would have scored 3 * 2 = 6 goals. Since the total number of goals scored by both players is 15, this scenario is not possible. Therefore, Skylar could not have scored 3 goals.
data are collected on the 35 students in a college history course. which of the following is not a variable for the data set? responses student birth month student birth month political affiliation of student political affiliation of student student age student age student address
Answers
The correct statement is-number of students in the data set
In research and data collecting, something that is being measured and whose values can change is referred to as a variable.
Given that we have a range of alternatives from January to December, the aforementioned example demonstrates how the student birth month is a variable. The student's ability to indicate whether they support particular political parties or not makes their political affiliation another variable. Since they are college students, the age of the student is another variable, with replies falling within a range of 20 to 25.
Since students will give different answers, whether they live at the same address or a different one, student address is also a variable.
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2)
a: b is 2:5 and b: c is 3:8
Work out a:c
Give your answer in its simplest form.
Answers
Answer:
a : c = 3 : 20
Step-by-step explanation:
Given ratios:
a : b = 2 : 5b : c = 3 : 8The value of b is 3 and 5.
The lowest common multiple of 3 and 5 is 15.
Multiply each ratio by a factor of 15 so that b is 15.
Multiply ratio a : b by 3:
⇒ a : b = 6 : 15
Multiply ratio b : c by 5:
⇒ b : c = 15 : 40
Therefore:
⇒ a : b : c = 6 : 15 : 40
So a : c is:
⇒ a : c = 6 : 40
Simplest form:
⇒ a : c = 3 : 20
Margin of error: 0.04; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 60%
A) 577 B) 1441 C) 996 D) 519
Answers
The required sample size of the given value is 577.
What is margin of error?
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.The formula to calculate the sample size :-
n = (p(1-p)((Zα/₂)/E)²
Given : Estimated proportion p = 0.60
Margin of error : E = 0.04
Significance level : α = 1-0.95 = 0.05
Critical value : Zα/₂ = 1.96
Now, the required sample size will be :-
n = (0.60)(0.11)(1.96/0.04)²
= 6.6 * (0.0784)²
= 0.57744
Hence, the required minimum sample size of the given is 577.
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m+ 1/3 < −2 1/4
Solve for m
Answers
To solve this inequality, we can start by converting the mixed numbers to improper fractions. The mixed numbers in this inequality are 1/3 and -2 1/4. The negative sign in front of 2 1/4 indicates that the resulting fraction will be negative. To convert 1/3 to an improper fraction, we can multiply the denominator (3) by the whole number (1) and add the result to the numerator (1). This gives us 1/3 = 4/3. To convert -2 1/4 to an improper fraction, we can multiply the denominator (4) by the whole number (-2) and add the result to the numerator (1). This gives us -2 1/4 = -9/4.
Next, we can combine the two fractions on the left side of the inequality by adding their numerators and denominators. This gives us m + 4/3 + -9/4. We can then simplify this expression by combining like terms. This gives us m - 9/12 + 4/3. We can further simplify this expression by adding the fractions with unlike denominators. To do this, we can find a common denominator by multiplying the two denominators together, which gives us 12 * 3 = 36. We can then convert the fractions to have this common denominator by multiplying the numerator and denominator of each fraction by the appropriate value. For m - 9/12 + 4/3, we have m - (9 * 3)/(12 * 3) + (4 * 12)/(3 * 12), which simplifies to m - 27/36 + 48/36. We can then combine like terms to get m + 21/36.
Finally, we can solve for m by moving all of the terms with m to one side of the inequality and all of the other terms to the other side. To do this, we can subtract 21/36 from both sides of the inequality, which gives us m + 21/36 - 21/36 < -2 1/4 - 21/36. This simplifies to m < -2 1/4 - 21/36, which we can further simplify by converting -2 1/4 - 21/36 to an improper fraction. To do this, we can multiply the denominator (4) by the whole number (-2) and add the result to the numerator (1), which gives us -2 1/4 = -9/4. We can then add -9/4 and -21/36 to get -9/4 - 21/36 = -105/36. Finally, we can convert this to a mixed number by dividing the numerator (-105) by the denominator (36) and taking the quotient (-2) as the whole number and the remainder (27) as the numerator of the fraction. This gives us -105/36 =
Please help I’m very confused on this question.
Answers
A survey of 20 randomly selected adult men showed that the mean time they spend per week watching sports on television is 10.53 hours with a standard deviation of 1.32 hours. Assuming that the time spent per week watching sports on television by all adult men is (approximately) normally distributed, construct a 90% confidence interval for the population mean,μ . Round your answers to two decimal places. Lower bound: Upper bound:
Answers
For a 90% confidence interval the upper and lower bound is 11.50 and 9.56 respectively.
What is confidence interval?Confidence interval means the probability that a population parameter will fall between a set of values.
What is the formula of confidence interval?The formula for confidence interval is C.I = u ± z (sd/[tex]\sqrt{n\\}[/tex] ) where u is the mean, sd is the standard deviation and z is the confidence level value. For an area of 90% around the mean, which makes 45% on each side, for the confidence level we will find the z-score at 0.45+0.5 = 0.95 area, and then double it since we need for both sides. At 0.95, the z-score is approximately 1.64. Thus, z is 3.28.
Plugging the values in the formula for C.I gives the upper bound as 10.53 + 0.968 = 11.50 and the lower bound as 10.53 - 0.968 = 9.56
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