The car will catch up with cyclist in 3 hours
What is time ?Time refers to the interval in seconds , minutes or hours it took for an event to take place
How to calculate How many hours it will take the car to catch up with cyclistInformation given for the question include
A cyclist has average speed of 9 miles per hour
A car leaves has average speed of 21 miles per hour
following same route when
The question is asking at what time will the distance be equal if the cyclists have advantage of 4 hours already
Calculation of distance covered by the cyclist
average speed = distance / time
distance = 9 mph * (x + 4)
Calculation of distance covered by the car
average speed = distance / time
distance = 21 mph * x
equating both gives
9 mph * (x + 4) = 21 mph * x
9x + 36 = 21x
36 = 21x - 9x
12x = 36
x = 3
hence the car will meet the cyclist in 3 hours
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a jury pool has 22 men and 16 women, from which 12 jurors will be selected. assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of
can you help show me the steps to solve this?
Answer:69
Step-by-step explanation8966966969996^996969969969699696996996969699696969699696699696966969669669669669669669669669
Find the possible outcomes for each event in rolling a number die. Then find the probability of each event as a fraction, decimal and percent.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for calculating probability
[tex]P(event)=\frac{number\text{ of favorable outcomes}}{number\text{ of possible outcomes}}[/tex]STEP 2: State the number of possible outcomes
[tex]\begin{gathered} A\text{ die has 6 faces numbered 1,2,3,4,5,6} \\ Therefore,\text{ the number of possible outcomes will be 6} \end{gathered}[/tex]STEP 3: Answer question A
Rolling a number less than 7
[tex]\begin{gathered} Numbers\text{ less than 7}\Rightarrow6,5,4,3,2,1 \\ n(numbers\text{ less than 7\rparen}\Rightarrow6 \\ \\ By\text{ substituting the values into the formula in step 1,} \\ P(Rolling\text{ a number less than 7\rparen}\Rightarrow\frac{6}{6}=1 \\ \\ Percentage\Rightarrow\frac{1}{1}\times100=100\% \end{gathered}[/tex]Hence,
Possible outcomes are 6,5,4,3,2,1
Probability = 1
Probability = 1.0 as decimal
Probability = 100% as percentage
STEP 4: Answer Question B
Rolling an 8
[tex]\begin{gathered} Possible\text{ outcomes}\Rightarrow8 \\ n(8)\Rightarrow0 \\ Probability=\frac{0}{8}=0 \\ Percentage=0\times100\%=0\% \end{gathered}[/tex]Hence,
Possible outcome is 0 since there is no face of the die having 8
Probability = 0
Probability = 0.0 as decimal
Probability = 0% as percentage
STEP 5: Answer Question C
Rolling a number greater than 4
[tex]\begin{gathered} Possible\text{ Outcomes}\Rightarrow5,6 \\ n(Possible\text{ outcomes\rparen}\Rightarrow2 \\ Probability=\frac{2}{6}=\frac{1}{3}\approx0.333 \\ Percentage=\frac{1}{3}\times100=\frac{100}{3}=33.33\% \end{gathered}[/tex]Hence,
Possible outcomes are 5,6
Probability = 1/3
Probability = 0.333 as decimal
Probability = 33.33% as percentage
STEP 6: Answer Question D
Rolling a number other than 6
[tex]\begin{gathered} Possible\text{ outcomes}\Rightarrow1,2,3,4,5 \\ n(Possible\text{ outcomes\rparen}\Rightarrow5 \\ Probability=\frac{5}{6}=0.8333 \\ Percentage=\frac{5}{6}\times100=83.33\% \end{gathered}[/tex]Hence,
Possible outcomes are 1,2,3,4,5
Probability = 5/6
Probability = 0.8333 as decimal
Probability = 83.33% as percentage
Model car is a 1/40 scale model expressed as a ratio
Answer:1:40
Step-by-step explanation:
the answer should be 1:40
Rectangles DEFG with vertices D(1,0) E(7,2) F(8, -1) and G (2, -3)
A. Translations along the the rule (x, y) —> (x -8 y -3)
Part A
[tex]D(1,0) \longrightarrow D'(1-8, 0-3)=D'(-7, -3)\\\\E(7,2) \longrightarrow E'(7-8, 2-3)=E'(-1, -1)\\\\F(8,-1) \longrightarrow F'(8-8, -1-3)=F'(0, -4)\\\\G(2,-3) \longrightarrow G'(2-8, -3-3)=G'(-6, -6)[/tex]
Part B
Reflecting over the x axis means [tex](x, y) \longrightarrow (x, -y)[/tex].
[tex]D'(-7, -3) \longrightarrow D''(-7, 3)\\\\E'(-1, -1) \longrightarrow E''(-1, 1)\\\\F'(0, -4) \longrightarrow F''(0, 4)\\\\G'(-6, -6) \longrightarrow G''(-6, 6)[/tex]
Paula measured the auditorium and made a scale drawing. The stage, which is 56 feet long in real life, is 84 inches long in the drawing. What scale did Paula use?
3 inches= ? feet
There are 2 feet in real life be 3 inches long in the scale drawing.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The stage, which is 56 feet long in real life, is 84 inches long in the scale drawing.
Let the x feet in real life be 3 inches long in the drawing.
According to the given question, we can write a ratio as
56 feet : 84 inches = x feet : 3 inches
⇒ 56 / 84 = x / 3
Apply the cross-multiplication operation,
⇒ 56 × 3 = x × 84
⇒ 168 = 84x
⇒ 84x = 168
⇒ x = 168 / 84
⇒ x = 2
Therefore, there are 2 feet in real life be 3 inches long in the scale drawing.
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professor horvat designs a study to assess the work satisfaction and home-life satisfaction of a group of graduate students. she administers the same measures of work and home-life satisfaction on two occasions, 1 year apart. she finds at both the first time point and the second time point there is a strong correlation between work satisfaction and home-life satisfaction. which type of correlations are these?
The type of correlation founded in the study by assessing the work and home life satisfaction measure identically at two occasions, a year apart, is a cross-sectional correlation.
Cross-sectional correlation is a non-experimental research design that uses data collected from a single time point. It is used to generate a static portrait of research variables. As opposed to serial correlation which is a correlation of one variable at different times, cross- sectional correlation is a correlation of two variables at the same time.
In the given study, professor measured the work satisfaction and home-life satisfaction at one time point and repeated it after a year at the second time point. She found a strong correlation between variable at both time points. Hence, it is cross-sectional correlation.
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GEOMETRY
Circle the one contradictory piece of information in each of the following sets of information
Answer:
Step-by-step explanation:
Item 1
<RSL is not ≅ < XYM
Item 2
< LST and < QRX are not supplementary (they are congruent)
Item 3
m < LST = 120 - there is no evidence for this.
Item 4
< JRS = <LST
so, If < LST = 120, then this can't be 195
In the figure below, AX'Y'Z' is a dilation of AXYZ. Find the scale factor of the dilation, andspirit as an enlargement or a reduction. What is the scale factor?What is the Classify?
The scale factor can be obtained by determining the ratio of the length of the sides of the old and new figures.
In other words, it can be obtained by stating that:
[tex]\text{scale factor=}\frac{lengthofsideoftriangleX^IY^IZ^I}{\text{length of side of triangle XYZ}}\text{ }[/tex]Specifically, we can say that:
[tex]\text{scale factor=}\frac{X^IY^1}{XY}=\frac{X^IZ^I}{XZ}=\frac{Y^IZ^I}{YZ}[/tex]Now, if each block (or cell) on the graph represents 1 units, we have that:
X'Y' = 10 units and XY = 5 units
Therefore:
[tex]undefined[/tex]Find the median and mean of the data set below:
20, 46, 20, 26
a=3,k=12,z=6,h=4 Evaluate algebraic expression
k-a+h
Answer:
[tex]k - a + h[/tex]
Step-by-step explanation:
Hope this helps you! :))
The perimeter of a rectangular garden is 252 feet. If the width of the garden is 53 feet , what is its length
The perimeter of a rectangle is given by:
[tex]P=2l+2w[/tex]Where:
P = perimeter = 252 ft
w = width = 5 ft
l = lenght
Then, substitute the values:
[tex]252=2l+2(53)[/tex]And solve for l:
[tex]\begin{gathered} 252=2l+106 \\ 252-106=2l+106-106 \\ 146=2l \\ \frac{146}{2}=\frac{2l}{2} \\ l=73 \end{gathered}[/tex]Answer: length = 73 ft
can you please answer work the math problem the easiest quick way please
Given: the three points are plotted on graph.
For the first point it is observed that,
For the x =3/2 the value is y=6/2
For second point ,
For x= 9/2 the y value is y=12/2
For the third point ,
For x= 15/2 the y value is y=18/2
According to obtained information it matched to option J)
Answer: Option J)
In triangle ABC measure of angle A equals 45°. The altitude divides the side AB into two parts of 20 and 21 units. Find BC.
In triangle ABC, BC = 29 units.
Given,
In Δ ABC, ∠A = 45°.
A perpendicular line segment traced from a triangle's vertex to its opposite side is said to be the triangle's altitude.
Let altitude meet AB on D.
So, AD = 20 units and DB = 21 units and ∠ADC = ∠BDC = 90°
In ΔADC,
tan A = DC/AD
tan 45° = DC/20
1 = DC/20
DC = 20 units
In ΔBDC,
BC² = BD² + DC² (Pythagorean Theorem)
= 21² + 20²
= 441 + 400
= 841
BC = √841
= 29
Hence, BC = 29 units.
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Carter wants to use the model above to solve 273 ÷ 13. Explain how he would find parts A, B, and C of the model. Unfortunately I can’t show the model because “it hurts their feelings”
Answer: The answer to the division problem is 21
Answer: I know 273 divided by 13 is 21 but without the model I don't know what else you need. sorry!
Step-by-step explanation:
by what factor does the intensity increase for each whole number increase in the richter scale?
Answer:
By adding the gravity of the earth ang subtracting the number of the enumeration and multiply the square root of need to be the first divorcee you know that I love ckicen nuggets
Step-by-step explanation:
Me to mama o sige na kain na kau
33% of millennials rely on blogs before making a purchase and eight
out of 10 millennials never buy anything without reading a review first.In a sample size of 75 Millennials, how many people use blogs to make a purchase?In a sample size of 75 Millennials, how many people never buy anything without reading a
review first?
24 millennials will use blogs to make a purchase and 60 millennials will never buy anything without reading a review first.
Here, we are given that 33% of millennials rely on blogs before making a purchase and eight out of 10 millennials never buy anything without reading a review first.
a. If there is a sample of 75 Millennials, out of these 33% will use blogs to make a purchase.
Thus,
33% of 75
= 33/100 × 75
= 33/4 × 3
= 99/4
= 24.75
Since, the number of millennials cannot be a decimal number, we approximate it to the lowest integer, that is, 24.
Thus, 24 millennials will use blogs to make a purchase.
b. Now, if there is a sample of 75 Millennials, out of these 8 out of 10 will never buy anything without reading a review first.
8 out of 10 in percentage terms will be-
8/10 × 100
= 80%
Thus,
80% of 75
= 80/100 × 75
= 80/4 × 3
= 20 × 3
= 60
Thus, 60 millennials will never buy anything without reading a
review first.
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Find MN such that LN = 5.7.
Line LN is compounded by segments LM and MN. The lenght of segment LM is fixed (1.3), and we need to find how long should segment MN be so the whole segment LN has a length of 5.7.
The length of segment LN is the sum of lengths of segments LM and MN. Writing it as an equation:
[tex]LN=LM+MN[/tex]We an replace the values we know in the equation:
[tex]5.7=1.3+MN[/tex]Now, we just need to solve for MN:
[tex]\begin{gathered} MN=5.7-1.3 \\ \\ MN=4.4 \end{gathered}[/tex]Segment MN should have a length of 4.4 for the segment LN to be 5.7. Correct answer is option D.
Josie sold 790 tickets to a local car show for a total of $4,390.00. A ticket for a Child costs $4.00 and adult ticket costs $7.00. How many of each ticket did she sell? A) Children’s ticket? B) Adult Ticket?
Let's define the following variables first.
A = number of tickets sold for adults
C = number of tickets sold for children
From the question, we can say that or form the following equations:
1. A + C = 790 tickets
2. $7A + $4C = $4, 390
The first equation can also be written as A = 790 - C. We can use this equation and replace "A" in the second equation.
[tex]7(790-C)+4c=4,390[/tex]From that, we can solve "C" by solving the equation formed above.
[tex]\begin{gathered} \text{Distribute 7 to the terms inside the parenthesis.} \\ 7(790)-7(C)+4C=4,390 \\ 5,530-7C+4C=4,390 \\ \text{Subtract 5,530 on both sides of the equation.} \\ -7C+4C=-1140 \\ -3C=-1140 \\ \text{Divide -3 on both sides.} \\ C=380 \end{gathered}[/tex]Therefore, 380 tickets for children were sold.
Since there are 790 tickets in total that are sold and 380 tickets for children were sold, we can say that 410 tickets for adult was sold.
[tex]\begin{gathered} A=790-C \\ A=790-380 \\ A=410 \end{gathered}[/tex]It took Brian 3 hours to drive to a rock concert. On the way home, he was able to increase his average speed by 23 mph and make the return drive in only 2 hours. Find his average speed on the return drive.The equation from part 2 is 3x=2(x+23)Step 3 of 3: Solve the equation found in part 2 for x. Use this information to answer the given word problem.
Answer:
69 mph
Explanation:
The equation that represents this situation is:
[tex]3x=2(x+23)[/tex]We are required to determine Brian's average speed on the return drive.
To do this, we first find the value of x.
[tex]\begin{gathered} \text{Open the bracket} \\ 3x=2x+46 \\ \text{Subtract 2x from both sides} \\ 3x-2x=46 \\ x=46\; \text{mph} \end{gathered}[/tex]Using the value of x, we find the average speed on the return drive.
[tex]x+23=46+23=69\text{mph}[/tex]Therefore, the average speed on the return drive will be 69 mph.
suppose that you need to build as many chairs as possible. each chair requires one seat, one back, and four legs. if you have 12 seats, 15 backs, and 44 legs, which of the chair components limits the number of chairs you can make? legs seats backs how many chairs can you make with the 12 seats, 15 backs, and 44 legs? what chair components will be leftover after making as many chairs as possible? seats and backs legs and backs seats and legs
The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.
What is meant by probability?The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.
The maximum number of chairs that can be made will be the minimum of the number of parts divided by the number of parts required for each chair, as calculated across the various types of parts required.
seats: 12 available, used 1 per chair: 12/1 = 12 chairs possible
backs: 15 available, used 1 per chair: 15/1 = 15 chairs possible
legs: 44 available, used 4 per chair: 44/4 = 11 chairs possible
The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.
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I NEED HELP WITH THIS ASAP!!!! The following diagram describes the mixture's volume of blue and red paint. What is the ratio of blue color to real paint in the mixture?
The ratio of blue color to red paint in the mixture is 5 :3.
What is the ratio?
Ratio expresses the relationship between two or more numbers. It shows the frequency of one value compared to the frequency of another value. The sign that is used to measure ratio is :.
In order to determine the ratio, count the number of blue tiles and the number of red tiles.
Number of blue tiles = 10
Number of red tiles = 6
The ratio of blue to red is 10 : 6. When expressed in its simplest form, it is 5 : 3.
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what is 1/3 of 9 cookies and lollipops
∵ 1/3 of 9 means multiply it by 9
[tex]\begin{gathered} \because\frac{1}{3}\times9=\frac{1\times9}{3}=\frac{9}{3} \\ \therefore\frac{1}{3}\times9=3 \end{gathered}[/tex]3 is 1/3 of 9 cookies and lollipops
Answer:
1/3 of 9 is 3.
Step-by-step explanation:
Think of it like this: what number can be added to itself 3 times to get 9? The answer is 3! 3 + 3 + 3 = 9. So, 1/3 of nine is 3 because 9 split into 3 sections would be 1/3 + 1/3 + 1/3 = 1 and 3 + 3 + 3 = 9. So, 1/9 simplified is 1/3!
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A tennis racket sells for $54.At the spring clearanceevent, the price is 30% lessthan the original. What isthe sale price?
We have
tennis racket price $54
Firs we need to obtain the 30 %
54*.30=16.2
then in order to know the sale price we need to substract the 30% of the original price
54-16.2=37.8
the sale price is $37.8
what is the equation of the line perpendicular to y = 1/2x+1 that contains the point ( - 2 ,1)
The linear equation perpendicular to y = 1/2x+1 that contains the point ( - 2 ,1) is:
y = -2x - 3
How to get the equation of the perpendicular line?Let's say that:
y = m*x + b
Where m is the slope and b is the y-intercept.
Is the line we want to find.
Two lines are perpendicular if the product between the slopes is -1, so this line is perpendicular to:
y = (1/2)*x + 1
Only if:
m*(1/2) = -1
m = -1*2 = -2
So the linear equation is of the form:
y = -2*x + b
If this line passes through (-2, 1), then:
1 = -2*(-2) + b
1 = 4 + b
1 - 4 = b
-3 =b
The linear equation is y = -2x - 3
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I need help understanding, how do I solve this?
3 – [–(–1)]
Answer:
3-[1]
3-1
2
Step-by-step explanation:
=//7777/))_+++++++4
-3a - 10 = 20
Solve the following equation
Answer:
a = -10
Step-by-step explanation:
-3a - 10 = 20
add 10 to both sides:
-3a - 10 + 10 = 20 + 10
-3a = 30
divide both sides by -3:
-3a/-3 = 30/-3
a = -10
Answer:
a=- 10
Step-by-step explanation:
-3a - 10 = 20
+10=+10
you end up with -3a=30
divide by -3 both side
a=-10
At a simple annual interest rate of 4.5%, how many years will it take Sam to earn $135 interest on an original deposit of $1,000?
A. 3
B. 4
C. 5
D. 6
Answer: A
Step-by-step explanation:
Interest = Principal * Rate * Time
135 = 1000 * 4.5% * T
135 = 1000 * 0.045 * T
135 = 45 * T
T = 135/45
T = 3 (A)
Here is a sketch of the unique triangles that can be
made with angle measures 80° and 20° and side
length 5.
PLEASE HELPPPP
ASAAAAPPPPP DUE AT END OF TODAY
Option (B) describes the correct unique possibilities of the given triangle.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. △ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same. Triangles can be divided into three types based on the lengths of their sides, and these are Scalene, Isosceles, and Equilateral.So, according to the given image:
We can easily observe that the triangle is an isosceles triangle with base angles being equal and the third angle being the smallest.Then, the correct option about the triangle will be an option (B).Therefore, option (B) describes the correct unique possibilities of the given triangle.
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PLEASE HELP ME. SERIOUSLY. I HAVE 30 MINUTES LEFT.
Let D be the dilation with center O and scale factor r>0 so that Dilation (P) = P' and
Dilation (Q) = Q'.
233.8
If |OQ|= 10 units, 10Q'] = 15 units, and IP'Q'] = 11.2 units, determine |PQ|. Round your
answer to the tenths place, if necessary.
incase you cant see, he right side is P, and below it is P1
Dilation factor is 3/2.
Define dilation factor.Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. According to Math Bits Notebook, the scale factor is equal to the ratio of these distances.
Given,
OQ = 10
OQ' = 15
Let dilation factor be r
OQ ×r = OQ'
10× r = 15
r = 3/2
Dilation factor is 3/2.
Coordinates of P = (-4, -3)
Coordinates of P' = (-6, -4.5)
b) ΔOPQ ≅ ΔOP'Q'
Congruent,
[tex]\frac{OQ}{OQ'}[/tex] = [tex]\frac{PQ}{P'Q'}[/tex]
[tex]\frac{10}{15}[/tex] = [tex]\frac{PQ}{11.2}[/tex]
PQ = 7.46
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