Marcus is playing dodge ball with hisfriends. He catches 2 out of every 5 ballsthrown in his direction. If he catches14 balls, how many balls were thrownat him?balls
Answers
Step 1
Given;
[tex]\begin{gathered} \text{Marcus is playing dodge ball with his friends.} \\ He\text{ catches 2 out of every 5 balls thrown in his direction.} \end{gathered}[/tex]Required; To find out how many balls are thrown at him if he catches 14 balls.
Step 2
There are two approaches to determine the number of balls thrown at Marcus
Approach 1
[tex]\begin{gathered} \text{Marcus catches 2 balls for every 5 balls thrown in his direction.} \\ we\text{ can draw up a table and add up 2 balls caught and 5 balls } \\ \text{thrown respectively until we arrive at 14 balls caught.} \end{gathered}[/tex]Draw the table;
we will now sum the total number of balls caught by Marcus and the total number of balls thrown at him to find out he had 35 balls thrown at him when 14 balls were caught by him.
Answer=35 balls
Approach 2
[tex]\begin{gathered} We\text{ will use the ratio} \\ \frac{2\text{ balls caught}}{14\text{ balls caught}}=\frac{5\text{ balls thrown }}{x\text{ balls thrown}} \\ \text{cross multiply} \\ 2x=5(14) \\ \text{simplify} \\ 2x=70 \\ \text{divide both sides by 2} \\ \frac{2x}{2}=\frac{70}{2} \\ x=35\text{ balls thrown} \end{gathered}[/tex]Hence, 35 balls were thrown at Marcus
Related Questions
The note A has a frequency of 1,760 hertz. The note D has a period of 1,175 hertz. Find theratio of A to D to two decimal places. Express the answer in integer ratio form.
Answers
Ratios
Note A has a frequency of
fa=1,760 Hz
Note D has a period of 1,175 hertz
(the previous data should be frequency, not period)
We are required to find the ratio of A to D. Let's call it r:
[tex]r=\frac{1,760^{\prime}}{1,175}[/tex]Dividing: r = 1.4978. Rounding to two decimal places:
r = 1.50
Now to express the answer in integer ratio form, we need to simplify the fraction.
First, we divide by 5 up and down:
[tex]r=\frac{352^{\prime}}{235}[/tex]There are no more common divisors for both numbers, thus the integer ratio form is r = 352/235
a tree that is 20 feet tall casts a shadow 30 feet long. a girl standing next to the tree has a shadow 9 feet long. how tall is the girl?
Answers
The shadow of the three is proportional to the shadow of the girl, then we can use a rule of three:
if x is the height of the girl: 20 is to 30 is the same as x is to 9
This can be written as:
[tex]\frac{20}{30}=\frac{x}{9}\Longrightarrow x=\frac{9\cdot20}{30}=\text{ 6}[/tex]Answer:
The girl is 6 feet tall
what is (x + 5)(2× - 3) = 0 in expanded form??
Answers
(x + 5)(2x -3) = 0
2x² - 3x + 10x - 15 = 0
2x² + 7x - 15 = 0
Answer:
2x² + 7x - 15 = 0
what does ☆ equal if the symbols below represents digits 0-9?
Answers
First, let's start from the sixth equation.
Since the parallelogram divided by the circle is equal the parallelogram, it means the circle has a value of 1.
Then, from the 7th equation, the pentagon minus the arrow is equal the pentagon, it means the arrow is equal 0.
From the 8th equation, the two curved arrows summed are equal 10, so the curved arrow is equal 5.
From the 2nd and 4th equations we can find that the triangle is equal 2.
Using the value of the pentagon from the 4th equation in the 3rd one, we have that 3 * moon is equal parallelogram, so the only option is:
moon = 3, pentagon = 6, parallelogram = 9.
From the 1st equation, the square is equal 8.
Finally, from the 5th equation, the arrow with circle is equal 7.
So we have:
pentagon = 6
parallelogram = 9
moon = 3
triangle = 2
arrow = 0
curved arrow = 5
arrow with circle = 7
circle = 1
square = 8
So the star is the missing algarism: 4
Solve for t and graph the solution.|t+ 4| < 2
Answers
The solution to the inequality is (-6, -2). The graph of the solution is attached below.
We are given an inequality. The inequality consists of a variable "t" and it also uses the modulus function. A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. The inequality is |t + 4| < 2. We can solve the inequality by expanding the modulus operator. The inequality becomes -2 < (t + 4) < 2. Now we will subtract 4 from all the sides in the inequality. The inequality is solved as -6 < t < -2. The interval notation for the solution is (-6, -2). The graph is attached below.
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selecting among the numbers 1 through 8 and repeating none of them, fill in the boxes below to make the sum as close as possible to one but not equal to one
Answers
We need ti fill in the boxes below, selecting among the numbers 1 through 8 and repeating none of them to make the sum as close as possible to 1 but not equal to 1.
First fraction could be 1/2
Now, the second fraction should be closer to 1/2 to make the sum as close as possible to 1, but not equal to 1.
We know that 3/6 = 1/2
So, 3/7 would be closer to 1/2
Therefore, the boxes could be filled as;
[tex]\frac{1}{2}+\frac{3}{7}[/tex]..
Write the ratio as a fraction in simplest form without any units.9 gallons to 28 quarts
Answers
Given
The ratio, 9 gallons to 28 quarts.
To find:
The ratio as a fraction in lowest term.
Explanation:
It is given that,
The ratio, 9 gallons to 28 quarts.
That implies,
[tex]\begin{gathered} 9\text{ }gallons\text{ }to\text{ }28\text{ }quarts=\frac{9\text{ }gallons}{28\text{ }quarts} \\ =\frac{9\times4\text{ }quarts}{28\text{ }quarts} \\ =\frac{9}{7} \end{gathered}[/tex]Hence, the simplest form of the ratio is 9/7.
Over the summer, Audrey had a job and earned $528. She spent $125.70 on a new bike and $85.09 for some new clothes. How much money does Audrey have left?
Answers
Step 1: Problem
Over the summer, Audrey had a job and earned $528. She spent $125.70 on a new bike and $85.09 for some new clothes. How much money does Audrey have left?
Step 2: Concept
Word problem on subtraction
Step 3: Method
Audrey total earning = $528
Money spent on new bike = $125.7
Money spent on new clothes = $85.09
Money left = 528 - 125.7 - 85.09
= $317.21
Step 4: Final answer
Audrey money left = $317.21
Options for all the three boxes are:neither student, Becky and Laura
Answers
The parent cosine function is given to be:
[tex]f(x)=\cos (x)[/tex]The graph of this function is shown below:
Laura's Function:
Laura's function is given to be horizontally compressed by a factor of 1/3 and reflected over the x-axis.
The rule for horizontal compression by a factor of 1/a is given to be:
[tex]f(x)\Rightarrow f(\frac{1}{a}\cdot x)[/tex]and the rule for reflection over the x-axis is given to be:
[tex]f(x)\Rightarrow-f(x)[/tex]Therefore, Laura's function will be:
[tex]f(x)=-\cos (3x)[/tex]The graph of the function will be:
Becky's Function:
Becky's function is given to be:
[tex]f\mleft(x\mright)=3\cos \mleft(x-\pi\mright)[/tex]The graph is given to be:
ANSWERS:
BECKY's GRAPH is the FIRST GRAPH
The SECOND GRAPH belongs to NEITHER
LAURA's GRAPH is the THIRD GRAPH
Simplify each expression using Product to a Power Property a. (9a)^2 b. ( 3x)^2
Answers
1) Let's simplify those expressions making use of exponents rules:
[tex](9a)^2=81a^2[/tex]Note that the exponent outside the parenthesis is 'distributed' over each term inside.
2) Similarly for the second expression we can state that:
[tex](3x)^2=9x^2[/tex]The diameters of ball bearings are distributed normally. The mean diameter is 125 mm and the standard deviation is 3 mm. Find the probability that the diameter of a selected bearing is greater than 127 mm. Round your answer to four decimal places.
Answers
Explanation
Given that the mean diameter is 125 mm and the standard deviation is 3 mm. We can find the probability that the diameter of a selected bearing is greater than 127 mm below.
We will first find the z score of the given value.
[tex]z=\frac{x-\mu}{\sigma}=\frac{127-125}{3}=\frac{2}{3}=0.66667[/tex]Using the z score calculator,
[tex]P\left(x>127\right)=0.2525[/tex]Answer: 0.2525
What is the perimeter of the figure2x + 3 inchesX- 6 inches
Answers
Perimeter of the figure = 6x - 6
Explanation:Perimeter = 2(length + width)
length = 2x + 3 inches
width = x- 6 inches
Perimeter = 2(2x + 3 + x- 6)
collect like terms in the bracket:
= 2(2x +x + 3 - 6)
= 2(3x - 3)
Expand the bracket:
Perimeter = 2 × 3x + 2× -3
Perimeter of the figure = 6x - 6
J is the midpoint of HK, H has coordinates (5,-3), and J has coordinates (7,3). Find the coordinates of K.The coordinates of K are
Answers
Answer:
The coordinates of K is;
[tex](9,9)[/tex]Explanation:
We want to find the coordinates of point K.
Given that J is the midpoint of HK and;
H has coordinates (5,-3)
J has coordinates (7,3).
The formula for calculating midpoint is;
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]where x1 and x2 are the x coordinates of the endpoints and y1 and y2 are the y coordinates of the endpoints.
To get the coordinates of one of the endpoints, we have;
[tex]\begin{gathered} x_2=2x-x_1 \\ y_2=2y-y_1 \end{gathered}[/tex]substituting the given coordinates of the mid point and endpoint;
[tex]\begin{gathered} x_2=2(7)-5 \\ x_2=14-5 \\ x_2=9 \end{gathered}[/tex][tex]\begin{gathered} y_2=2(3)-(-3) \\ y_2=6+3 \\ y_2=9 \end{gathered}[/tex]Therefore, the coordinates of K is;
[tex](9,9)[/tex]Challenge The value of a baseball player's rookie card began to increase once the player retired. When he retired in 1996 his card was worth $9.17. The value has increased by $1.65 each year since then, Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2006? Express the relationship with an equation. y=?
Answers
$151.31. Not proportional.
y= 9.17 +1.65x
1) Gathering the data
1996 Retired $ 9.17
9.17(1.65)^x
2) Since the value of that card has been increasing 1.65 yearly, then we can write the following equation:
[tex]y=9.17+1.65x[/tex]For y= Value, and x =years
Let's find out the value of the card in 2006, i.e. 10 years later. Plug x=10 into the above function:
[tex]\begin{gathered} y=9.17+1.65x \\ y=9.17+1.65(10) \\ y=9.17+16.5 \\ y=151.305\approx y=151.31 \end{gathered}[/tex]3) Hence, the value of the card in 2006 is $151.31
(rounded off to the nearest hundredth)
And since the initial value is $9.17, then it is not a proportional relationship since an initial value of a proportional is always 0.
how do you dilate with a scale factor of -1/2Coordinates (-2,8)
Answers
Multiply the coordinates by the scale factor.
(-2,8) = (-2x-1/2, 8x-1/2) = (1,-4)
In which quadrant, or on which axis, does the terminal side of angle (- 100straight pi) lie?
Answers
The given angle is
[tex]\theta=-\frac{100}{\pi}[/tex]First, we have to transform this angle into degrees. We know pi=180°, so
[tex]\theta=-\frac{100}{180}=-\frac{50}{90}=-\frac{5}{9}=-0.56[/tex]The given angle is placed on the first quadrant.Assuming that the angle is starting on the positive x-axis.
A survey wanted to determine if there was a relationship between the number of joggers who used a local park for exercise and the temperature outside. The data in the table display their findings.Use graphing technology to create a scatter plot of the data.What is the slope of the line of best fit and what does it mean in this context? Is it realistic?
Answers
Step 1
In order to find the slope of the line of the best fit, we must graph the points given.
Step 2
From the image above we can conclude that the equation of the line is;
[tex]y=0.410045x-2.8757[/tex]The slope is, therefore;
[tex]0.410045[/tex]The Slope (or Gradient) we call m, represents the change in y-value per unit change in x-value. In the case of this survey, the slope represents the increase in the number of joggers per degree rise in temperature.
From the calculated slope, there are about 0.4 more joggers for every degree rise in temperature. Using whole numbers to represent this, we can multiply the slope by 5:
[tex]0.4\times5=2[/tex]Therefore, there are 2 more joggers for every 5°F increase in temperature.
The function h is defined below.xh (x) =2+5x-- 142x- 81Find all values of × that are NOT in the domain of h.If there is more than one value, separate them with commas.
Answers
We want to find the value of x that is not in the domain of the function;
[tex]h(x)=\frac{x^2+5x-14}{x^2-81}[/tex]The value of x that will make h undefined is the value that makes the denominator zero.
Therefore;
[tex]\begin{gathered} x^2-81=0 \\ x^2=81 \\ x=\pm9_{} \end{gathered}[/tex]Therefore, the values not in the domain is +9 and -9
The total annual sales for Herman's Hardware Store was $1,246,135 and the total accounts receivable was $41,728. What was the average collection period to the nearestwhole day?12 days14 days18 days24 daysNone of these choices are correct.
Answers
The average collection Period formula is
[tex]\text{Average collection period=}\frac{Account\text{ receivable}}{\frac{Annual\text{ sales}}{365}}[/tex][tex]\begin{gathered} \text{Annual sales=\$1,246,135} \\ \text{Account receivable =\$41,728} \end{gathered}[/tex]Substitute the values above in the average collection period
[tex]\begin{gathered} \text{Average collection period =}\frac{41728}{\frac{1246135}{365}} \\ =\frac{41728}{3414.06} \\ =12.222 \\ \approx12days \end{gathered}[/tex]Hence the average collection period to the nearest whole day is 12 days
Please help me and explain how to find the result
Answers
A family consumes 1.2kg of rice a day
If the family have 30ky of rice
Let the number of days be x
The minimum number of days required for the amount of rice remaining not to be more than 6kg can be expressed below as
[tex]30-1.2x\le6[/tex]Solve for x by collecting like terms
[tex]\begin{gathered} 30-1.2x\le6 \\ 30-6\le1.2x \\ 24\le1.2x \\ 1.2x\ge24 \\ \text{Divide both sides by 1.2} \\ \frac{1.2x}{1.2}\ge\frac{24}{1.2} \\ x\ge20\text{ days} \end{gathered}[/tex]Hence, the minimum number of days required for the amount of rice remaining not to be more than 6kg is 20 days
unsure about this one tried and couldn’t seem to figure it out
Answers
Given:
The figure contains the rectangle and half-circle.
The perimeter of the half-circle is,
[tex]\begin{gathered} \text{Half}-\text{circle}=\pi r+d \\ r=\frac{d}{2}=\frac{8}{2}=4 \\ \text{Half}-\text{circle}=\pi(4)+8 \\ =3.14\times4+8 \\ =20.56 \end{gathered}[/tex]The perimeter of the figure is,
[tex]P=10+8+10+20.56=48.56[/tex]Answer: P = 48.56 ft.
Question #10: A pizza restaurant sells a personal square pizza (5 inch side) for $4. What should the cost of a large square pizza (12 inch side) be, so that both pizzas cost the same amount per square inch?
Answers
The per square-inch cost of the first kind of pizza is $0.16 to maintain this ratio for 12-inch side pizza the cost must be $23.04.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
Cost of first pizza = $4
Area = 5 x 5 = 25 square inch
Per square cost = 4/25 = $0.16
With this ratio,
Cost of 12 inches side = 12 x 12 x 0.16 = $23.04
Hence "The per square-inch cost of the first kind of pizza is $0.16 to maintain this ratio for 12-inch side pizza the cost must be $23.04".
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A builder is buying boxes of nails. She has $187 to spend and each box of nails costs $4. How many boxes of nails can the builder buy?42503746
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To find How many boxes of nails can the builder buy divide the total she has into the cost of each box:
Then, she can buy 46 boxes of nailsif 5 pounds of apples cost 5.50,then what is the cost of 1 pound of apples
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The cost of 1 pound of apple is 1.10
Here, we want to calculate the cost of 1 pound of apples given the cost of 5 pounds
From the question;
5 pounds = 5.5
1 pound = x
Thus, we have that;
[tex]\begin{gathered} 5\text{ }\times\text{ x = 1 }\times\text{ 5.5} \\ \\ 5x\text{ = 5.5} \\ \\ x\text{ = }\frac{5.5}{5} \\ \\ x\text{ = 1.1} \end{gathered}[/tex]I need help with this
Answers
Ok, so
We have the following expression:
We're going to multiply all terms inside the bracket by "-x", and we obtain:
So, the answer is B.
if y=3x+4 and y=2x+8, find the value of both x and y.
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having that x=4, we get that
[tex]y=2\cdot4+8=16[/tex]Help with number one a and b is both parts of number one
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Design A. The garden is 9 ft by 12 ft.
Design B. The garden is a circle of radius 5 ft
Area of garden A:
[tex]A_A=9\times12=108[/tex]Area of garden B:
[tex]A_B=\pi\left(5\right)^2=25\pi\approx78.54[/tex]The areas are:
Design A = 108 square ft
Design B ≈ 78.54 square ft
Note: The area of garden B can also be expressed in exact form as 25π square ft
solve for x[tex] \frac{x + 3}{2} + \frac{2x}{7} = 7[/tex]just need some help with this
Answers
Here, we are to calculate for the value of x.
We start by finding the Lowest common multiples of both fractions. The lowest common multiple of both fractions is 14
Now, we can multiply each of the terms in the question by 14. Thus, we have;
14(x + 3)/2 + 14(2x/7) = (7 * 14)
7(x + 3) + 2(2x) = 98
Opening the brackets, we have;
7x + 21 + 4x = 98
Collect like terms;
7x + 4x = 98 - 21
11x = 77
x = 77/11
x = 7
question will be in picture
Answers
Consider the guven system of equations,
[tex]\begin{gathered} x-y=-1 \\ 2x+y=4 \end{gathered}[/tex]It is asked to find the correct graph which represent the solution of this system.
Logic: Find the solution and see which graph gives the same solution.
Add the equations,
[tex]\begin{gathered} (x-y)+(2x+y)=-1+4 \\ 3x+3 \\ x=1 \end{gathered}[/tex]Substitute this value in the first equation,
[tex]\begin{gathered} 1-y=-1 \\ y=1+1 \\ y=2 \end{gathered}[/tex]Thus, the given system has a unique solution (1,2).
Now, observe that only the graph given in option (c) shows the line intersecting at point (1,2).
Therefore, option (c) is the correct choice.
The lines represented by the equations y = 1/2x-8 and 2y+4x=10
Answers
The first equation is in slope-intercept form but the second equation is not. Therefore, our first step is to bring 2y+4x=10 into slope-intercept form.
Subtracting 4x from both sides gives
[tex]2y=10-4x[/tex]finally, dividing both sides by 2 gives
[tex]y=-2x+5[/tex]Now, that we have the equation in slope-intercept form, let us compare their slopes to see how they relate to each other.
The lines are perpendicular if the slope of one line is negative of the reciprocal of the other.
Now, -2 is negative of the reciprocal of 1/2. Meaning if you take the reciprocal 1/2, then multiply it by -1 you will end up with -2.
Since the slope of a negative reciprocal of each other, the lines are perpendicular.