The converse, inverse and contrapositive of each conditional statement include:
Converse: If two angles have a common side, then they are adjacent.Inverse: If two angles are not adjacent, then they do not have a common side.Contrapositive: If two angles do not have a common side, then they are not adjacent.What is a conditional statement?
A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."
Where:
P and Q represent sentences.
In this scenario, we would write the converse, inverse and contrapositive of each conditional statement as follows:
Converse: If two angles have a common side, then they are adjacent.Inverse: If two angles are not adjacent, then they do not have a common side.Contrapositive: If two angles do not have a common side, then they are not adjacent.Read more on conditional statement here: brainly.com/question/16951916
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Correctly explains how to estimate 33% of 87.
3abc
What is the coeficient of c?
Answer:
3
Step-by-step explanation:
3 is the coefficient of c as it is a constant, whereas a and b are variables, subject to change.
This year you earned $75,500. Last year you earned $72,400. What was the rate of change on your earnings since last year
Answer:
4.28%
Step-by-step explanation:
We Know
Last year you earned $72,400
This year you earned $75,500
What was the rate of change in your earnings since last year?
We Take
(75,500 ÷ 72,400) x 100 ≈ 104.28%
Then We Take
104.28 - 100 = 4.28%
So, the earning increased by about 4.28%.
Tyler's brother earns $14 per hour. The store offers him a 5% increase in wages per hour. After the raise, how much will tyler's brother make per hour?
After the raise, Tyler's brother will make $14 x 1.05 = $14.70 per hour.
Answer:
14 x 1.05 = 14.70
Step-by-step explanation:
(6,0) and (7,0).calculate the slope of the line with these two points
hello
to solve this problem, we can simply use the formula of slope of a line
\(\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}\)now we can identify our values
\(\begin{gathered} y_2=0 \\ x_2=7 \\ y_1=0 \\ x_1=6 \end{gathered}\)\(\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0-0}{7-6} \\ m=\frac{0}{1} \\ m=0 \end{gathered}\)from the calculations above, the slope of the line from the given points is 0
Write an equation of the line with the given slope, m, and y-intercept (0,b).
m = 2, b = 1
Answer:
\(\boxed {\boxed {\sf y=2x+1}}\)
Step-by-step explanation:
Equations of line are written in slope-intercept form, or
\(y=mx+b\)
where m is the slope and b is the y-intercept. We know that the slope is 2 and the y-intercept is 1, because we are given:
\(m=2 \\b=1\)
Substitute the values into the formula.
\(y=2x+1\)
The equation of the line is y=2x+1
A spinner with 10 equal sized slices has 4 yellow slices, 3 red, and 3 blue slices. Kala spun the dial 1000 times and got the following results.
Kala spun the spinner 1000 times and got the following results:
- Yellow: 400 times
- Red: 300 times
- Blue: 300 times
1. Calculate the amount of sales tax:
- The item costs $350 before tax.
- The sales tax rate is 14%.
- To find the sales tax amount, multiply the cost of the item by the tax rate:
Sales tax = $350 * 0.14 = $49.
2. Determine the total cost of the item including tax:
- Add the sales tax amount to the original cost of the item:
Total cost = $350 + $49 = $399.
3. Analyze the spinner results:
- The spinner has 10 equal-sized slices.
- There are 4 yellow slices, 3 red slices, and 3 blue slices.
- Kala spun the dial 1000 times.
4. Calculate the frequency of each color:
- Yellow: Kala got 400 yellow results out of 1000 spins.
- Red: Kala got 300 red results out of 1000 spins.
- Blue: Kala got 300 blue results out of 1000 spins.
5. Calculate the probability of landing on each color:
- Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.
- Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.
- Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.
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For which store location does 68% of the data lie between $19,371.18 and $22,295.48? A. location C B. location D C. location B D. location A
The store location for which % of the data lies between $19,371.18 and $22.295.48 is location C
What is standard deviation?You should be aware that Standard deviation explains the relation of data with mean.
For normal distributions, 68% of the data lies under one SD from the mean. Two standard deviations is within 95%, and three standard deviations would take up to 99%.
This implies that on taking (mean + SD) and (mean - SD), 68% of data would cover these two numbers.
Add and subtract SD from the mean to check which location will give $19,371.18 and $22.295.48.
For location A, we have
M-SD=23,124.70-1553.43=21,571.27
M SD = 23,124.70 + 1,553.43 = 24,678.4
For location B, we have
M - SD = 24,842.18 - 1,617.20 = 23,224.98
M + SD = 24, 842.18 + 1,617.20 = 26,459.38
For location C, we have
M - SD = 20,833.33 - 1,462.15 = 19,371.18
M + SD = 20,833.33 + 1,462.15 = 22,295.48
This implies the store location is C
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Correct question:
The owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. She calculated the mean and standard deviation of the monthly profit, in dollars, for each location, as shown in the table.
For which store location does 68% of the data lie between $19,371.18 and $22,295.48?
If the owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. The location that 68% of the data lie between $19,371.18 and $22,295.48 is: A. Location C.
How to find the location?Location A:
Mean -Standard Deviation
=23,124.70-1553.43
=21,571.27
Mean + Standard Deviation
= 23,124.70 + 1,553.43
= 24,678.4
Location B:
Mean -Standard Deviation = 24,842.18 - 1,617.20
Mean -Standard Deviation = 23,224.98
Mean + Standard Deviation
= 24, 842.18 + 1,617.20
= 26,459.38
Location C:
Mean - Standard Deviation
= 20,833.33 - 1,462.15
= 19,371.18
Mean + Standard Deviation
= 20,833.33 + 1,462.15
= 22,295.48
Therefore the correct option is C.
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The complete question is:
The owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. She calculated the mean and standard deviation of the monthly profit, in dollars, for each location, as shown in the table.
Location A Location B Location C Location D
Mean = 23,124.70
SD = 1,553.43 Mean = 24,842.18
SD = 1,617.20 Mean = 20,833.33
SD = 1,462.15 Mean = 21,432.82
SD = 1,512.10
For which store location does 68% of the data lie between $19,371.18 and $22,295.48?
LOOK AT THE PICTURE!!
Answer:
it is data
Step-by-step explanation:
just look at it and describe its properties
Bye,
Canus Lupus
what is the range of the following data set?
Answer: The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.
What is the slope of the line that contains the points (2, −7) and (−1, 5)?
−4
negative one fourth
one fourth
4
the slope is -4
hope this helps!!
Answer:
the slope is -4
Step-by-step explanation:
2x+4y=11 how do you solev thia?
A rectangular patio has a length of (1 + 2x) yards and a width of (2 - 3x) yards. Which correctly describes the area and perimeter of the patio?
Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.
What is a yard?A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.
The area of the rectangular patio is given by multiplying its length by its width, so the area is:
A = (1 + 2x)(2 - 3x)
Now using distributive property we get,
A = 2 - 3x + 4x - 6x²
Simplifying further, we get:
A = -6x² + x + 2
Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.
To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:
P = 2(1 + 2x) + 2(2 - 3x)
Simplifying this expression, we get:
P = 2 + 4x + 4 - 6x
P = 6 - 2x
Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.
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2 questions.
Find the lenght and width
Find the admission price for an adult ticket and student ticket.
1) The length of the rectangle is 15 feet and its width is 9 feet.
2) The admission price for an adult ticket is $10 and a student ticket is $6.
How to solve the problems?1) We shall use the formula for the area of a rectangle to find the length and the width:
A = l * w
where:
A = Area.
l = length
w = width.
Given:
l = 6 feet more than the width.
A = 135 feet square meter
First, we write an equation for the area like this:
(w + 6) * w = 135
Expanding the equation:
w² + 6w - 135 = 0
Next, solve the quadratic equation by factoring:
(w - 9)(w + 15) = 0
So either w - 9 = 0 or w + 15 = 0. This means that either w = 9 or w = -15. Since the width cannot be negative, we have w = 9.
Finally, we shall find the length since we know the width. This can be done by using the fact that it is 6 feet more than the width:
l = w + 6 = 9 + 6 = 15
So, the length is 15 feet and the width is 9 feet.
2) We can find the admission price for an adult ticket and a student ticket by using Mathematical operators:
Let,
a = an adult ticket price
s = a student ticket price
From the given information, we get these equations:
5a + 11s = 116
3a + 4s = 54
Next, solve by substitution.
Solving for 'a' in the second equation:
a = (54 - 4s) / 3
Then, substitute the second expression for 'a' into the first equation:
5((54 - 4s) / 3) + 11s = 116
Multiply both sides by 3:
5(54 - 4s) + 33s = 348
Finally, expand and simplify:
270 - 20s + 33s = 348
13s = 78
s = 6
So, a student ticket costs $6.
Plug this value into either equation to get the adult ticket price:
3a + (4 * 6) = 54
3a + 24 = 54
3a = 30
a = 10
So, an adult ticket costs $10.
Therefore,
1) The length of a rectangle is 15 feet and the width is 9 feet
2) The admission price for an adult ticket is $10 and that of a student is $6
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Find the measure of the angle at the center of atom B inside the triangle
The measure of the angle having the question mark, found using the law of sines is ? ≈ 140°
What is the law of sines?The law of sines states that the sine of an interior angle of a triangle is proportional to the the length of the side opposite to the angle.
The given parameters are;
The radius of circle A = 6.4
The radius of circle B = 4.0
The radius of circle C = 3.0
The measure of angle at C = 24°
The length of the segment AB = 6.4 + 4 = 10.4
According to the law of sines, we have;
\(\dfrac{sin(A)}{a} = \dfrac{sin(B)}{b} = \dfrac{sin(C)}{c}\)
Where;
a = The length of the side opposite angle ∠A
b = The length of the side opposite angle ∠B
c = the length of the side opposite angle ∠C
From the diagram, the side opposite angle ∠C, is AB, which by comparison indicates that when side c = AB = 10.4
c = 10.4
Similarly, the side opposite angle ∠A = a = BC = 4 + 3 = 7
a = 7
The known information are therefore; ∠C = 24°, a = 7, c = 10.4
\(\dfrac{sin(A)}{a} = \dfrac{sin(C)}{c}\)
\(\dfrac{sin(A)}{7} = \dfrac{sin(24^{\circ})}{10.4}\)
\(sin(A) = \dfrac{sin(24^{\circ})}{10.4}\times 7\)
\(\angle A = arcsine \left( \dfrac{sin(24^{\circ})}{10.4}\times 7\right)\)
∠A + ∠B + ∠C = 180° (angle sum property of a triangle)
∠B = 180° - (∠A + ∠C)
Which gives;
\(\angle B = 180^{\circ} -\left(24^{\circ} + arcsine \left( \dfrac{sin(24^{\circ})}{10.4}\times 7\right)\right) \approx 140^{\circ}\)
The measure of the angle is ∠B ≈ 140°
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Deon plans to ride a 15 mile bicycle trail. If his average speed is 20mi/h, which equation can he use to find the time t, in hours, for the ride?
Answer
15=20t
Step-by-step explanation:
Answer:
t = 15 / 20
Step-by-step explanation:
Given:
Distance traveled by Deon to ride a bicycle trail = 15 mile
Average speed of Deon to ride a bicycle trail = 20 mi/hour
Step-by-Step:
Let 'T' be the time taken to ride the bicycle trail.
We will use distance speed formula to write the equation to find the time 'T' in hours, for the ride.
\(Distance=\frac{Speed}{Time}\)
Distance = 15 miles
Speed = 20 miles / hour
Time = 15 / 20
Assuming time is t, the formula would be:
t = 15 / 20
"t = 15 mi/ 20 mi/hr " will help Deon calculate the time he will take.
Therefore, t = 15 / 20
point(m,5)lies on the line given by the equation 5x-y=20.find m
Answer:
m = 5
Step-by-step explanation:
given point (m,5) lies on the line 5x-y=20,( x , y )
here x is m and y is 5, lets put it in the equation to solve:
5x-y=20
5(m) - 5 = 20
5m = 20 + 5
5m = 25
m = 25/5
m = 5
Please answer the 2 questions I put. Please show your work in the answers.
On a school bus, 22 of the 40 students are in window seats. What percent of the students are in window seats?
Only 6 of the 75 trees in a park are at least 30 feet tall. What percent of the trees are under 30 feet tall?
Answer:
75% of what number is 24? 32. Yesterday, 8% of the 150 6th graders were late. How many 6th graders were late? ... On a school bus, 22 of the 40 students are in window seats. What percent of the students are at a window seat? 55%. Write as a fraction in simplest form. 0.8%. 1/125.
Step-by-step explanation:
If 32 of the 92 people who swim at the ymca are adults , what is the ratio of adults to children who swim at the ymca. Write the ratio in the lowest terms as a fraction or with a colon
Answer:
8:23
Step-by-step explanation:
You can solve this problem by repeatedly dividing both numbers by 2. After dividing it by 2 a few times, you will find that you can't divide it anymore. Then your answer is whatever you numbers you have, in this case 8 and 23.
Which expression can be used to find m pls help
Answer:
∠ U = 22.62°
Step-by-step explanation:
We can use the trigonometric expression to find ∠U by using the ratio:
sin(θ) = opposite/ hypotenuse
=> sin ∠U = 7.5/ 19.5
=> ∠ U = \(sin^{-1}\)( 7.5/ 19.5)
∴ ∠ U = 22.619° ≈ 22.62°
Translate the sentence into an equation.
Two times the sum of a number and 4 equals 9.
Use the variable y for the unknown number.
Answer:
The equation for this sentence is: 9 = 2(4y)
Answer:
2(y + 4) = 9Step-by-step explanation:
Two times the sum of a number and 4 equals 9:
2(y + 4) = 9What is the least common multiple of 6x^2+39x and 6x^2+54x+84?
Answer: 6x\(6x{2}+93x-126andx{2}+84\)
Step-by-step explanation: The only thing you do is just to keep multiplying until you get your answer.
how many solutions are there to each of these equations?
Answer:
first one, put value of x= -3 and y = 0
second one, pit vale of x=7 and y= -7
Step-by-step explanation:
first one,
-14(-3) -20(0) =42
or, 42-0 = 42
or, 42 = 42
proved
second one,
-14(7) -20(-7) = 42
or, -98 + 140=42
or, 42 = 42
proved
24 children were asked which is their favourite colour from a choice of red, blue
green or yellow. Their answers are shown below:
Blue
Red
Red
Green
Yellow
Red
Red
Red
Complete the frequency table.
Colour
Red
Blue
Red
Yellow
Red
Blue
Green
| Yellow 1111
Green
Blue
Green
Blue
Tally
Un Un
un
Analysing and Displaying Data
Yellow
Yellow
Blue
Red
Frequency
Red
Red
Blue
Yellow
The frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).
What is a conditional relative frequency?It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell to total frequency.
It is given that:
24 children were asked which is their favourite colour from a choice of red, blue
green or yellow
From the data given in the question.
Red : 6
Blue: 4
Green: 8
Yellow : 1 (half of 2)
Pink: 1 (half of 2)
Thus, the frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).
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On the same coordinate plane mark all points (x y) that satisfy the rule y=3x-2 SHOW GRAPH
Answer:
*View the attached graph*
Step-by-step explanation:
Hope it helps!
salesperson earns $345 for selling $2300 in merchendice find the commison rate
Answer:
The commission rate is 15%
Step-by-step explanation:
commission = commission rate x sales
where the commission rate is expressed as a decimal.
In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:
345 = commission rate x 2300
To solve for the commission rate, we can divide both sides by 2300:
commission rate = 345/2300
Simplifying this expression, we get:
commission rate = 0.15
So, the commission rate is 15%
Can someone help me pls
The correct solution of the expression 3/4 ( 6x - 4) = 1/2 (x + 4) with the property that justify each step is shown below.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 3/4 ( 6x - 4) = 1/2 (x + 4)
Now, Solve the expression as;
⇒ 3/4 ( 6x - 4) = 1/2 (x + 4)
⇒ 9/2x - 3 = 1/2x + 2 By Distributive property
⇒ 9/2x - 3 - 1/2x = 1/2x + 2 - 1/2x Subtraction property of equality
⇒ (9/2 - 1/2)x - 3 = 2 Combine like terms
⇒ 4x - 3 = 2 Subtraction property
⇒ 4x - 3 + 3 = 2 + 3 Addition property of equality
⇒ 4x = 5
⇒ 1/4 × 4x = 1/4 × 5 Multiplication property of equality
⇒ x = 5/4
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Which numbers lie between -2 and -3 on the number line? Select all that apply.
Answer:
-2.5, -2.02, -11/4
Step-by-step explanation:
Any number beginning with -2 will be the answer. -11/4 is -2.75 when converted to a decimal!
Use the Empirical Rule to answer each question.
During 1 week an overnight delivery company found that the weights of its parcels were normally distributed, with a mean of 24 ounces and a standard deviation of 6 ounces.
(a) What percent of the parcels weighed between 12 ounces and 30 ounces? (Round your answer to one decimal place.)
(b) What percent of the parcels weighed more than 42 ounces? (Round your answer to two decimal places.)
The percent of the parcels weighed between 12 ounces and 30 ounces will be 81.86%. And the percentage of the parcels weighing more than 42 ounces will be 0.13%
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
During 1 week an overnight delivery company found that the weights of its parcels were normally distributed, with a mean of 24 ounces and a standard deviation of 6 ounces.
Then the percent of the parcels weighed between 12 ounces and 30 ounces will be
When x = 12, then we have
z = (12 - 24) / 6
z = -2
When x = 30, then we have
z = (30 - 24) / 6
z = 1
Then we have
P(12 < x < 30) = P(-2 < z < 1)
P(12 < x < 30) = 0.81859
P(12 < x < 30) = 81.86%
Then the percentage of the parcels weighing more than 42 ounces will be
When x = 42, then we have
z = (42 - 24) / 6
z = 3
Then we have
P(x > 42) = P(z > 3)
P(x > 42) = 1 - P(z < 3)
P(x > 42) = 0.0013499
P(x > 42) = 0.13%
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Which of the q-values satisfy the following inequality?
6 - 3q <_ 1
Choose all that apply
q = 0
q = 1
q = 2
Answer:
Step-by-step explanation: q=o
Answer:
c is the answer.
Step-by-step explanation: