The measure of angle A will be 61°
The sum of A and B is 122°
The sum of A B and C is 151°
How to calculate the angle?It should be noted that complementary angles have an angle of 90°.
Therefore, the value of A will be:
= 90° - 29°
= 61°
The value of B will be:
= 90° - 29 = 61°
The value of A and B will be:
= 2 × 61°
= 122°
The value of A B and C will be:
= 122 + 29
= 151°
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Drag a statement or reason to each box to complete this proof.
If-3(x+8)= -21, then z = -1.
Statement
1.
2. -~(38) =
3.
4.z+8-8-7-8
5. x=-1
Subtraction Property of Equality
Reason
Given
Simplifying
Simplifying
Distributive Property of Equality
-3(z+8)= -21
Division Property of Equality
z+8=
Answer:
Step-by-step explanation:
OMG!! im doing the same thing, i am struggling
the demand curve for hummus has a constant slope of -2. what can you say about the price elasticity of demand for hummus with this information?
Based on the given information that the demand curve for hummus has a constant slope of -2, we can say that the price elasticity of demand for hummus is relatively elastic. This means that a small change in price will result in a relatively larger change in the quantity demanded of hummus.
In other words, consumers are sensitive to changes in the price of hummus and are likely to reduce their consumption if the price increases, and vice versa.
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The price elasticity of demand for hummus cannot be determined solely from the information provided, as it depends on both the slope and the price-quantity relationship.
The price elasticity of demand (Ed) is a measure of how responsive the quantity demanded of a good is to a change in its price. It is calculated using the formula:
Ed = (% change in quantity demanded) / (% change in price)
Since the demand curve for hummus has a constant slope of -2, this tells us that for every unit increase in price, the quantity demanded decreases by 2 units. However, to calculate the price elasticity of demand, we also need information about the price and quantity levels.
The slope of the demand curve alone does not provide enough information to determine the price elasticity of demand. The elasticity varies along the curve, being more elastic at high prices and low quantities, and less elastic at low prices and high quantities.
While the slope of the demand curve for hummus is -2, this information alone is not sufficient to determine the price elasticity of demand. Additional information about the price and quantity levels is needed to calculate the elasticity accurately.
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After Mrs. Fisher lost 20% of her investment, she had $34,000. What was Mrs. Fisher's original investment? The original value of the investment was $ 8..
Mrs. Fisher's original investment was $42,500. To find Mrs. Fisher's original investment, we can set up an equation based on the information provided.
Let's denote Mrs. Fisher's original investment as X.
According to the problem, Mrs. Fisher lost 20% of her investment, which means she retained 100% - 20% = 80% of her original investment.
We can set up the equation as follows:
80% of X = $34,000
To solve for X, we need to convert the percentage to decimal form. 80% is equal to 0.8.
0.8X = $34,000
Now, we can solve for X by dividing both sides of the equation by 0.8:
X = $34,000 / 0.8
X = $42,500
Therefore, Mrs. Fisher's original investment was $42,500.
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in rolling 2 fair dice what is the probability of a sum greater than 3 but not exceeding 6
We can list all possible outcomes in a table and count the number of outcomes that meet the criteria. There are 9 such outcomes, which gives a probability of 9/36, or 1/4.
To calculate the probability of rolling a sum greater than 3 but not exceeding 6 with 2 fair dice, we first need to determine the total number of possible outcomes when rolling the dice. Since each die has 6 possible outcomes, there are a total of 6 x 6 = 36 possible outcomes when rolling 2 fair dice.
| Die 1 | Die 2 | Sum |
|-------|-------|-----|
| 1 | 3 | 4 |
| 1 | 4 | 5 |
| 1 | 5 | 6 |
| 2 | 2 | 4 |
| 2 | 3 | 5 |
| 3 | 1 | 4 |
| 3 | 2 | 5 |
| 4 | 1 | 5 |
| 5 | 1 | 6 |
There are a total of 9 outcomes where the sum is greater than 3 but not exceeding 6. Therefore, the probability of rolling a sum greater than 3 but not exceeding 6 with 2 fair dice is 9/36, which simplifies to 1/4.
The probability of rolling a sum greater than 3 but not exceeding 6 with 2 fair dice can be calculated by dividing the number of outcomes where the sum is greater than 3 but not exceeding 6 by the total number of possible outcomes.
There are a total of 36 possible outcomes when rolling 2 fair dice, as each die has 6 possible outcomes. To determine the number of outcomes where the sum is greater than 3 but not exceeding 6, we can list all possible outcomes in a table and count the number of outcomes that meet the criteria. There are 9 such outcomes, which gives a probability of 9/36, or 1/4.
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The probability of the sum of two dice being greater than 3 but not exceeding 6 is 1/3 as there are 12 successful outcomes out of a total 36.
Explanation:This question is about the probability in rolling two dice.
When rolling two fair dice, there will be total 36 possible outcomes (6 possible outcomes for one die times 6 for the second die). The outcomes where the sum is greater than 3 but not exceeding 6 are: {1,3}, {1,4}, {1,5}, {2,2}, {2,3}, {2,4}, {3,1}, {3,2}, {3,3}, {4,1}, {4,2}, {5,1}. There total 12 such outcomes.Therefore, the probability of this event is 12/36 or 1/3.
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Jenny is organising a party,
She buys some paper plates and some plastic cups.
Paper plates are sold in packs.
There are 25 plates in a pack,
Each pack costs 78p.
Plastic cups are sold in packs.
There are 35 cups in a pack.
Each pack costs £1.10
Jenny buys exactly the same number of plates and cups.
What is the least amount of money she pays?
5 Marks
PLEASE HELP FOR BRAINLEST!!!!
Answer:
repel and attract is correct answer
Answer:
repel; attract
Step-by-step explanation:
think of magnets, N and N repel and N and S attract
Help me please please
HELPPPPPPPPPPPPPPPPPPPPP
Answer:
the answer to number 2 is: y=-4x-26
The answer to number 3 is y=5/2x+54
Step-by-step explanation:
two customers took out home equity loans.
Cathy took out a 10-year loan for $20,000 and paid %5.20 annual simple interest
Steven took out a 15-year loan for 20,000 and paid %4.80 annual simple interest
what is the difference that Cathy and Steven paid for their loans?
The difference in the amount paid by Cathy and Steven is $4000.
What is the difference in the amounts?
Simple interest is when the interest that is paid on the loan of a customer is a linear function of the loan amount, interest rate and the duration of the loan.
Simple interest = amount borrowed x interest rate x time
Simple interest of Cathy = $20,000 x 0.052 x 10 = $10,400
Simple interest of Steven = $20,000 x 0.048 x 15 = $14,400
Difference in interest = $14,400 - $10,400 = $4000
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Find the root of the following function
Solve sin x = 2-3 by using False position method.
The root of the equation sin(x) = 2 - 3 is x = 0, determined using the false position method.
To find the root of the equation sin(x) = 2 - 3 using the false position method, we need to perform iterations by updating the bounds of the interval based on the function values.
Let's define the function f(x) = sin(x) - (2 - 3).
First, we need to find an interval [a, b] such that f(a) and f(b) have opposite signs. Since sin(x) has a range of [-1, 1], we can choose an initial interval such as [0, π].
Let's perform the iterations:
Iteration 1:
Calculate the value of f(a) and f(b) using the initial interval [0, π]:
f(a) = sin(0) - (2 - 3) = -1 - (-1) = 0
f(b) = sin(π) - (2 - 3) = 0 - (-1) = 1
Calculate the new estimate, x_new, using the false position formula:
x_new = b - (f(b) * (b - a)) / (f(b) - f(a))
= π - (1 * (π - 0)) / (1 - 0)
= π - π = 0
Calculate the value of f(x_new):
f(x_new) = sin(0) - (2 - 3) = -1 - (-1) = 0
Since f(x_new) is zero, we have found the root of the equation.
The root of the equation sin(x) = 2 - 3 is x = 0.
The root of the equation sin(x) = 2 - 3 is x = 0, determined using the false position method.
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Find the exact values of tan (2 arcsin in) without a calculator.
The exact value of tan(2arcsin(x)) is 2x / √(1 - x²), where |x| ≤ 1.
To find the exact value of tan(2arcsin(x)), we start by considering the definition of arcsin. Let θ = arcsin(x), where |x| ≤ 1. From the definition, we have sin(θ) = x.
Using the double angle identity for tangent, we have tan(2θ) = 2tan(θ) / (1 - tan²(θ)). Substituting θ = arcsin(x), we obtain tan(2arcsin(x)) = 2tan(arcsin(x)) / (1 - tan²(arcsin(x))).
Since sin(θ) = x, we can use the Pythagorean identity sin²(θ) + cos²(θ) = 1 to find cos(θ). Taking the square root of both sides, we have cos(θ) = √(1 - sin²(θ)) = √(1 - x²).
Now, we can determine the value of tan(arcsin(x)) using the definition of tangent. We know that tan(θ) = sin(θ) / cos(θ). Substituting sin(θ) = x and cos(θ) = √(1 - x²), we get tan(arcsin(x)) = x / √(1 - x²).
Finally, substituting this value into the expression for tan(2arcsin(x)), we obtain tan(2arcsin(x)) = 2x / (1 - x²).
Therefore, the exact value of tan(2arcsin(x)) is 2x / √(1 - x²), where |x| ≤ 1.
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does the equation y 2 + x = 1 represents a function y in terms of x?
Answer:
nah it dosent
Step-by-step explanation:
ya hope it helps watever
two groups of students were taught statistics using two different methods. the data indicate that group a achieved significantly higher scores than group b. the differences in the scores were not based on the teaching methods, but rather were caused by extraneous variables. drawing the incorrect conclusion that the teaching method caused the result in this case is an example of:
Drawing the incorrect conclusion that the teaching method caused the difference in scores, when in fact it was caused by extraneous variables, is an example of a Type I error, also known as a false positive. It occurs when a hypothesis is rejected even though it is true.
what is variables?
In mathematics, statistics, and programming, a variable is a named value that can take on different values or values of different types. In other words, a variable is a symbol or a container that holds a value or a reference to a value. Variables are used to store and manipulate data in computer programs, mathematical formulas, and statistical analyses. In programming, variables can be used to store and manipulate data such as numbers, strings of text, and arrays of values. In mathematics and statistics, variables can represent numerical quantities or categories that are being measured or observed.
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Circle D is shown with the measures of the minor arcs. Which angles are congruent?
A.) EDH and FDG
B.) FDE and GDH
C.) GDH and EDH
D.) GDF and HDG
The correct option is B) FDE and GDH, as their corresponding angles have the same intercepted arc and, therefore, are congruent.
To determine which angles are congruent in circle D, we need to analyze the given information about the measures of minor arcs. Since minor arcs are measured in degrees, we can use the following properties:
1. When two arcs are congruent, their corresponding central angles are also congruent.
2. The measure of a central angle is equal to the measure of its intercepted arc.
Given these properties, let's examine the answer choices:
A) EDH and FDG: We cannot determine their congruency based solely on the measures of the minor arcs.
B) FDE and GDH: These angles have the same intercepted arc, so they are congruent.
C) GDH and EDH: The intercepted arcs for these angles are different, so they are not congruent.
D) GDF and HDG: These angles have the same intercepted arc, so they are congruent.
Therefore, the correct option is B) FDE and GDH, as their corresponding angles have the same intercepted arc and, therefore, are congruent.
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identify an equation in point-slope for the line parellel to y= 1/2 x-7 that passes through (-3 , -2)
Answer:
y+2=1/2(x+3)
Why?
Point slope form is written as (y-y1) = m(x-x1) with y1 being the value of y at a certain point, x1 being the value of x at a certain point, and m being slope. y1 and x1 are given to us by the point (-3, -2) letting us know that y1=-2 and x1=-3. The only thing left to find is slope. Parallel lines have the same slope. If the line we are trying to find is parallel to the one given in the question, we just need to find the slope of the equation given. That equation is given in slope-intercept form which is y = mx + b. m is still slope so we can see that the slope is 1/2. Now we can plug m, x1 and y1 into the point slope form equation to get y + 2 = 1/2(x + 3)
Billys empolyer for 65% of his annual health insurance permiu. Billy has the rest deducted equal amounts from his paycheck. If Billy has $105.73 withheld from his paychecks twice each month, how much dose his employrt contribute twards his health insuranceon an annual basis.
Answer:
His employer contributes with $4712.53 towards his health insurance on an annual basis.
Step-by-step explanation:
With the information provided, you know that Billy's employer pays 65% of his health insurance premium and you can subtract this from 100% to know the percentage that Billy has to pay:
100%-65%=35%
Also, the information states that Billy has $105.73 withheld from his paychecks twice each month and you can multiply this for 24 to find the total amount that he pays per year and that represents 35%:
$105.73*24=$2537.52
Finally, you can use a rule of three to found the amount that represents 65% which would be what his employer pays given that $2537.52 represent 35%:
2537.52 → 35%
x ← 65%
x=(2537.52*65)/35
x=$4712.53
According to this, the answer is that his employer contributes with $4712.53 towards his health insurance on an annual basis.
Determine the volume of the cylinder
Answer:
about 904.78
Step-by-step explanation:
πr^2h pi(6)^2 * 8
Sam had 8819 grams of salt. He mixed 1715 grams of salt into a pot of soup he was cooking. Before serving the soup, he added 1158 grams of salt. About how much salt does Sam have left? Choose the best estimate.
Answer:
6000
Step-by-step explanation:
2000+1000=3000
9000-3000=6000
Side note: I'm not sure if this is 100% correct because you didn't give the choices
Answer:
60
Step-by-step explanation:
You have $175.29 in a savings account. You deposit an additional $48.75. How much more do you need to save to buy the cell phone?
Price: $249.99
Include the steps
Answer:
Step-by-step explanation:
So in your account you got $175.29
Then you deposit mean increase the amount of money in your account by $48.75
So: 175.29+48.75 = 224.04
The price is $249.99
So: 249.99 - 224.04 = $25.95
You need to save $25.95 in order to buy your cell phone
To buy the cellphone of worth $249.99, additional $25.95 are required.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
Given that,
The price of cellphone = $249.99
The amount in saving account = $175.29
Additional amount deposit in account = $48.75
Total amount in account after deposit = 175.29 + 48.75 = 224.04
Since, the price of cellphone is $249.99
And the amount in account = 224.04
So the more amount required = 249.99 - 224.04 = 25.95
To buy the cell phone $25.95 are required.
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69 POINTS!! PLS HELP!! PLATO
if f(x)=the square root of x, which equation describes the graphed function?
Answer:
i think it’s C
Step-by-step explanation:
-f(x) represents -square root of x, so i plugged negative square root of x subtracted by three into desmos and it matches the graph !
Answer:
y = -f(x)-3
Step-by-step explanation:
Just took the edmentum/plato test and I got it right. I also included my answer
a random sample of 24 cars found the average tire pressure was 22 psi with a standard deviation of 5 psi. safety manuals suggest the tire pressure should be at 28 psi. is there enough evidence to say at the 9% significance level that the average is less than 28?
Yes, there is enough evidence to say at the 9% significance level that the average is less than 28
Sample Size, n = 24
Sample Mean , x = 22
Standard Deviation s = 5
Significance Level α = 9% = 0.09
μ₀ : μ = 28
t- test statistics is,
t = x - μ / (s√n)
= 22-28/(5√24)
= -6/(5√24)
t = -0.24494
P-value is,
Degrees of freedom (df) = n-1 = 24-1 = 23
P-value = p(t<-0.24494)
= 0.0035
Therefore p-value is 0.0035
p-value<α, reject μ₀
There is sufficient evidence to support the claim.
A standard deviation (or σ) is a proportion of how distributed the information is corresponding to the mean. A low standard deviation implies information is bunched around the mean, and exclusive expectation deviation shows information is more fanned out.
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he function f(x) is shown on the graph. On a coordinate plane, a curved line shaped like a w, labeled f of x, crosses the x-axis at (negative 2, 0), (negative 1, 0), crosses the y-axis at (0, 12), and crosses the x-axis at (2, 0) and (3, 0). What is f(0)?
Based on the given information and the graph of f(x), the value of f(0) is undefined as the graph does not intersect the x-axis at x = 0.
To determine the value of f(0), we need to find the corresponding y-coordinate when x is equal to 0. From the given information, we know that the graph of f(x) crosses the y-axis at the point (0, 12). This means that when x is equal to 0, the y-coordinate is 12.
Since the graph of f(x) is shaped like a "w," it implies that the function has multiple x-intercepts. We are given that the graph crosses the x-axis at (-2, 0), (-1, 0), (2, 0), and (3, 0).
The graph of the function can be visualized as follows:
|
12 | .
| . .
| . .
| . .
|_____________
-2 -1 0 1 2 3
We can observe that f(0) is not defined for x = 0 since the graph does not cross the x-axis at x = 0. Therefore, there is no y-coordinate corresponding to f(0).
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2.2. South African friends of the Netherlands couple departed from Pretoria at 04h30am to spend the holiday with them. Their journey is described as follows: On their way from Polokwane they took the turn-off to the R521 route. Rest for 45 minutes at Dendron and took 15 minutes to do someshopping and till up the car's fuel tank at All days. 2.2.1. If the scale of the map is given as 1: 3 000 000 and the distance measured on the map between Beitbridge and Musina is 1,3 cm. calculate (in km) the actual distance between Beitbridge and Musina. ● (3)
The actual distance between Beitbridge and Musina is 3,900,000 kilometers.
To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.
The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.
The measured distance on the map between Beitbridge and Musina is 1.3 cm.
To find the actual distance, we can set up a proportion using the scale:
1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.
Simplifying the proportion, we have:
1 / 3,000,000 = 1.3 / x.
Cross-multiplying, we get:
x = (1.3 * 3,000,000) / 1.
x = 3,900,000 / 1.
x = 3,900,000 km.
The actual distance between Beitbridge and Musina is 3,900,000 kilometers.
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What is the formula for the margin of error?
Answer:
\(ME =\frac{z*s}{\sqrt{n}}\)
Step-by-step explanation:
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings
To find margin of error, you need
Get the population standard deviation (σ) and sample size (n)n = sample size
Take the square root of your sample size and divide it into your population standard deviationσ = population standard deviation Multiply the result by the z-score consistent with your desired confidence interval according to the following table:z = z-score
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The bends on a track for car racing are semicircular and the track is banked at an angle of 28
0
to the horizontal. Suppose the radius of the curvature of the bends is 120 m. a) At what speed can a racing car and a driver of mass 800 kg take these bends even when there is no friction between the car and the track? b) If the car speed is twice of that in (a). (i) draw the free-body diagram of the car (ii) Find the value of the frictional force f.
The bends on a track for car racing are semicircular, and the track is banked at an angle of 28.0° to the horizontal. Suppose the radius of the curvature of the bends is 120 m.
a) The formula to calculate the minimum velocity is given as follows:Vmin = √(rgtanθ)Where;Vmin is the minimum velocity needed to stay on the track;g is the acceleration due to gravity;r is the radius of the turn;θ is the angle of banking.r = 120 m, θ = 28.0°, and g = 9.8 m/s²Substitute the values into the formula, we get;Vmin = √(rgtanθ)=√(9.8 m/s² * 120 m * tan(28.0°))=40.6 m/sTherefore the minimum velocity the car should maintain is 40.6 m/sb) If the car speed is twice that in (a).
(i) The free-body diagram of the car is as shown below;
(ii) The value of the frictional force f is as follows;There are two forces acting on the car, namely; the normal force and the gravitational force. When the car moves at a constant speed around the bend, the centrifugal force Fc is also acting towards the center of the circular path. The centrifugal force Fc is given by the formula;Fc = mv²/rWhere;F c is the centrifugal force;m is the mass of the carv is the velocity of the car in m/sr is the radius of the curve.
Therefore;f = F s, max= μsNWhere;Fs, max is the maximum static frictional force that can be applied;N is the normal force acting on the car;μs is the coefficient of static friction.Because the car is not sliding, the maximum frictional force that can act is equal to the centripetal force, Fc.Thus;Fs, max = F c= 21,333.3 NThe frictional force f can now be determined as;f = Fs, max= μsN= 21,333.3 N= μsmgCosθwhere m is the mass of the car, and g is the acceleration due to gravity.
Substitute the values into the formula;μ s = f/mgCosθ= 21,333.3 N / 800 kg * 9.8 m/s² * Cos(28.0°) = 0.58Therefore the coefficient of static friction is 0.58.
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Samir and Kai are learning how to roller skate at the skate city roller rink. Samir has skated y laps around the rink. Kai has skated 4 fewer laps than Samir. write an expression that shows how many laps Kai has skated around the rink.
Answer:
x=y-4
Step-by-step explanation:
If Samir has skated y laps around the rink, then Kai has skated y - 4 laps around the rink.
So the expression that shows how many laps Kai has skated around the rink is: x=y-4
Answer:
Step-by-step explanation: patience. wyd here.
but the answer is x=y-4
When Micaela runs the 400 meter dash, her finishing times are normally distributed with a mean of 81 seconds and a standard deviation of 1.5 seconds. What percentage of races will her finishing time be faster than 79.5 seconds, to the nearest tenth
Answer:
Step-by-step explanation:
a class consist of 12 boys of whom 5 are perfects. how many committee of 8 can be formed if its to have; a) 3 prefects b) at least 3 prefects
Step-by-step explanation:
a) To form a committee of 8 with 3 prefects, we need to choose 3 prefects from the 5 available prefects, and 5 non-prefects from the remaining 7 boys. We can do this by using the combination formula:
Number of ways = (Number of ways to choose 3 prefects) × (Number of ways to choose 5 non-prefects)
Number of ways to choose 3 prefects from 5 = C(5, 3) = 10
Number of ways to choose 5 non-prefects from 7 = C(7, 5) = 21
Therefore, the total number of committees of 8 with 3 prefects that can be formed is:
Number of ways = 10 × 21 = 210
b) To form a committee of 8 with at least 3 prefects, we need to consider two cases: one where we choose exactly 3 prefects, and one where we choose all 5 prefects. We can calculate the number of ways for each case using the combination formula:
Number of ways to choose exactly 3 prefects and 5 non-prefects = C(5, 3) × C(7, 5) = 210
Number of ways to choose all 5 prefects and 3 non-prefects = C(5, 5) × C(7, 3) = 35
Therefore, the total number of committees of 8 with at least 3 prefects that can be formed is:
Number of ways = (Number of ways to choose exactly 3 prefects and 5 non-prefects) + (Number of ways to choose all 5 prefects and 3 non-prefects)
Number of ways = 210 + 35 = 245
Which of the following is not a factor in capacity planning?
a) approach used to measure capacity
b) economies of scale
c) prepare to deal with capacity in "chunks"
d) proximity to suppliers
e) identify the best operating level
The option that is not a factor of capacity planning is the option d
d) Proximity to suppliers
What is capacity planning?The process of ascertaining the production capacity an organization needs in order to meet changing demand for the products and services of the organization is known as capacity planning.
The factors considered in capacity planning are factors which include the capacity measurement approach, the economies of scale, preparedness to deal with the capacity in chunks, and activities towards identifying the best operating level.
Therefore, from the listed options, the option that is not a factor in capacity planning is the option (d) proximity to suppliers
Other aspects of the operations of an organization, such as supply chain management and logistics can be affected by the proximity of suppliers, but the proximity of suppliers is not directly linked to the determination process for the production capacity needed to meet the market demand.
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How many numbers of the set {1, 2, 3, 4, . . . , 297, 298, 299, 300} are multiples of 10 but not multiples of 15?
Answer:
I get 20
Step-by-step explanation:
While there probably is some logical way to go about this I just did it in excel
screenshot below
Answer:
20
Step-by-step explanation:
10
20
40
50
70
80
100
110
130
140
160
170
190
200
220
230
250
260
280
290