A pitcher needs more than one pitch to be effective. Dizzy uses his changeup only half as much as his fastball, and to save his arm, he throws a slider a third as much as his fastball. In a 110-pitch game, how many sliders would he throw?
In Dizzy's 110-pitch game, he threw 20 sliders. The answer was found by setting up and solving algebraic equations based on the information given in the question.
Explanation:This question is about using algebra to solve word problems. Let's denote the number of fastballs Dizzy throws as F, the number of changeups as C, and the number of sliders as S.
According to the question, Dizzy throws his changeup half as much as his fastball (C = 0.5F) and his slider a third as much as his fastball (S = F/3). We also know the total number of pitches (110) is the sum of F, C, and S pitches (110 = F + C + S).
We then substitute the expressions for C and S from our first two equations into our third equation to get: 110 = F + 0.5F + F/3. Solving this equation gives us F = 60. We substitute F = 60 into S = F/3 to find that Dizzy threw 20 sliders in the game.
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please help I have 2 pages to do!
A baseball has a diameter of 5.1 inches. Find the volume of the baseball. Round your answer to the nearest tenth. Use 3.14 for pi
A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of a house.
-When the company spends 2 hours to clean floors and 3 hours to clean the rest of a house, the total charge is $84.
-When the company spends 1 hour to clean floors and 4 hours to clean the rest of a house, the total charge is $87.
Which ordered pair represents the hourly charges to clean floors and to clean the rest of the house?
A. (12, 20)
B. (15, 18)
C. (18, 15)
D. (20, 12)
Note: Please show work. My teacher checks it.
The hourly charges to clean floors and to clean the rest of the house are $15 and $18, respectively. We determine this by setting up a system of equations from the provided scenarios and solving for x and y.
To solve for the hourly charges to clean floors (x) and to clean the rest of the house (y), we need to set up two equations based on the information provided:
2x + 3y = 84 (from the first scenario)1x + 4y = 87 (from the second scenario)Let's solve this system of equations step by step.
Step 1: From the second equation, we can express x in terms of y:
x = 87 - 4y
Step 2: Substitute this expression for x in the first equation:
2(87 - 4y) + 3y = 84
Which simplifies to:
174 - 8y + 3y = 84
Combining like terms gives us:
-5y = -90
Step 3: Solve for y:
y = 18
Step 4: Now, plug the value of y back into the expression for x:
x = 87 - 4(18)
x = 15
Therefore, the hourly charges to clean floors and to clean the rest of the house are $15 and $18 respectively, which corresponds to option B. (15, 18).
Help me asap please !!
A bag contains 8 blue marbles, 6 green marbles, 12 yellow marbles, and 10 orange marbles. A marble is drawn at random from the bag.
What is the probability that the marble drawn will not be blue?
A.) 29
B.) 34
C.) 79
D.) 78
Answer:
C
Step-by-step explanation:
I got it right and here is proof
If it is blurry, just press it and it will be non-blurry
if LuxRide's revenues in London grow by 20% next year, what will their market share be?
Could anyone help me with these?
Question 5 of 5 At 7:00 a.m., the temperature was 8°C. What was the temperature at midnight if the temperature was 10° lower? A. −18° C B. −2° C C. 2° C D. 18° C
What is the area of sector GPH? the angle inside the circle measures 80º and the radius from p to h is 15
Answer:
The area of sector GPH is equal to [tex]50\pi\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=15\ units[/tex]
substitute
[tex]A=\pi(15)^{2}=225 \pi\ units^{2}[/tex]
[tex]360\°[/tex] subtends the complete circle of area [tex]225 \pi\ units^{2}[/tex]
so
By proportion
Find the area of sector GPH
[tex]\frac{225 \pi}{360}\frac{\ units^{2} }{degrees} =\frac{x}{80}\frac{\ units^{2} }{degrees}\\ \\x=80*225\pi /360\\ \\x=50\pi\ units^{2}[/tex]
Can somebody please help me, I’m stumped. Please explain easily to
What is the area of a circle that has a circumference of 48 feet?
The opening in a rectangular door frame measures 9 feet by 3 feet. Each of the four doors described in the table measures 9 feet by 3 feet, but have different diagonal lengths. Which door will fit in the rectangular opening?
Door 1: 10 ft
Door 2: 3 square root 10ft
Door 3: 6 square root 2ft
Door 4: 12ft
Answer:B
Step-by-step explanation:
2 trifles cost 7 pounds how much does 6 cost
Cost of 6 trifles is 21 pound
Given that;Cost of 2 trifles = 7 pound
Find:Cost of 6 trifles
Computation:Cost of 6 trifles = 6[7 / 2]
Cost of 6 trifles = [3][7]
Cost of 6 trifles = 21 pound
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Robbie, Jennie, Willie, and Kylie played a numbers game. Jennie picked a number but did not tell her friends. Robbie and Willie both picked a number as well, and Jennie described their numbers like this to Kylie.
Robbie picked a number that is nine more than four times Jennie's number.
Willie picked a number that is two less than three times Robbie's number.
Deciding to call her number, n, Jennie asked Kylie to write an expression that describes Willie's number.
Kylie came up with two expressions that equal Willie's number.
What are the equations?
Answer:
1. 3(4n+9)-2
2. 3*13n-2
Step-by-step explanation:(*)This symbol that looks like a little star means multiplication.
The two equations that describe Willie's number are W = 12J + 25 and W = 12J + 34
What is Expression?An expression is combination of variables, numbers and operators.
Robbie's number = 4J + 9, where J is Jennie's number.
Now we can use this expression to find Willie's number:
Willie's number = 3(4J + 9) - 2 = 12J + 25
So one equation that describes Willie's number is:
W = 12J + 25
Kylie found another expression that equals Willie's number, so we can find it by solving for J in Robbie's expression and substituting it into Willie's expression:
Robbie's number = 4J + 9
4J = Robbie's number - 9
J = (Robbie's number - 9)/4
Substitute this expression for J into Willie's expression:
W = 12J + 25
W = 12[(Robbie's number - 9)/4] + 25
W = 3(Robbie's number - 9) + 25
W = 3(4J + 9 - 9) + 25 (substituting 4J + 9 for Robbie's number)
W = 12J + 34
So another equation that describes Willie's number is:
W = 12J + 34
Therefore, the two equations that describe Willie's number are W = 12J + 25 and W = 12J + 34
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One ounce is about the same as 0.06 pound. What is 0.06 written as a fraction?
Answer:
[tex].06 = \frac{6}{100} = \frac{3}{50} [/tex]
Ella surveyed the students at her school to find out if they like math and/or science. The table below shows the results of the survey:
Like Math Do Not Like Math Total
Like Science 41 22 63
Do Not Like Science 7 31 38
Total 48 53 101
If a student likes science, what is the probability that student does not like math?
14.5%
18.4%
34.9%
65.1%
Answer:
34.9
Step-by-step explanation:
Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle BDC, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by _______________. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel. Which phrase best completes the student's proof?
Final answer:
The triangles ABD and CDB are congruent by the Side-Angle-Side (SAS) postulate, leading to the conclusion that quadrilateral ABCD is a parallelogram.
Explanation:
The triangles ABD and CDB can be proved congruent by the Side-Angle-Side (SAS) postulate. Since side AB is parallel to side DC, the alternate interior angles angle ABD and angle BDC are congruent. With both triangles sharing side DB and having equal sides AB and DC, the two triangles satisfy the conditions of the SAS postulate.
By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) principle, angles DBC and ADB are congruent as well as sides AD and BC. Since angle DBC and angle ADB form a pair of alternate interior angles, this implies that AD is congruent and parallel to BC. This leads to the conclusion that quadrilateral ABCD is a parallelogram, characterized by its opposite sides being equal and parallel.
A is 60% of B , B is 30% of C , what percentage of C is A? show working out and circle the correct answer: 18%, 28%, 30%, 90%
can someone please help me i got stuck in this question
Explain how to write an inequality to model the problem.
The winning baseball team scored more than 5 runs. as in 5 < P
Answer:
Identify the variable as the number of runs. Identify the inequality symbol needed as greater than. Identify the constant as 5 runs. Write the inequality as r > 5.
Step-by-step explanation:
The inequality that represents the situation "The winning baseball team scored more than 5 runs" is (r > 5) where r represents the total runs scored by the team and this can be determined by using the given data.
Given :
The winning baseball team scored more than 5 runs.
The following steps can be used to determine the inequality that represents the given situation:
Step 1 - Let the total runs scored by the baseball team be 'r'.
Step 2 - Now, it is given that the winning baseball team scored more than 5 runs, the inequality that represents this situation is:
[tex]r > 5[/tex]
Greater than sign represents that the team scores more than 5 runs.
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Lorena has two pieces of ribbons. One piece is 3 meter 14 centimeter long. The other piece is 8 meters 24 centimeters long. How many centimeters of ribbon does Lorena have in all
what is the slope of the line through (6,9) and (7,1)
Find the length of the leg of a 16 90 45 triangle
First 5 multiples of 6: 6, 12, 18, 24, 30 First 5 multiples of 9: 9, 18, 27, 36, 45 What is the least common multiple (LCM) of 6 and 9?
Solution:
We are given the first five multiples of 6 and 9.
First 5 multiples of 6: 6, 12, 18, 24, 30 First 5 multiples of 9: 9, 18, 27, 36, 45If we look carefully, we can see that the smallest number that is common in both multiples is 18.
First 5 multiples of six: 6, 12, 18, 24, 30 First 5 multiples of nine: 9, 18, 27, 36, 45Thus, the LCM of 6 and 9 is 18.
LCM is lowest common multiple
Let's check
2|6,9
3|3,9
3|1,3
LCM=2(3)(3)=18
Anthony brings 4 bags of popcorn to a meeting. The bags of popcorn are all the same size. There are 14 people at the meeting. Each person eats the same amount of popcorn, and all of the popcorn is eaten. What fraction of a bag of popcorn did each person eat?
NEED HELP ASAP
Which of the following expressions is equivalent to (-7)(-7)(-7)?
3 · -7
-7 · 3
(-7)3
3-7
According to the order of operations, which of the following operations should be completed first in the following expression?
2(5 - 3)^2 + 6^2
multiply (5 - 3) by 2
square (5 - 3)
simplify (5 - 3)
add (5 - 3) to 6^2
Select all that apply.
Which expressions are equal to "five to the third power"?
5^3
3 · 3 · 3 · 3 · 3
5 · 5 · 5
125
15
243
3^5
The expression -8 · -8 · -8 · -8 can be expressed as _____.
-8^4
(-8)^4
-(8^4)
What is the value of -6^2?
-36
36
-12
12
Find the value of |5| - 4(3^2 - 2).
-11
-33
7
-23
Evaluate 8 ÷ -2 · 4^2 + 9.
-100
-55
73
-23
Simplify -5^2 + 8|-1| + (-3).
30
14
-20
-36
Answer:
The answers are solved below.
Step-by-step explanation:
we have to solve the given expressions
Part A: The expression (-7)(-7)(-7)
[tex] (-7)(-7)(-7)=(-1)^37^3[/tex]
Option 3 is correct
Part B: [tex]2(5 - 3)^2 + 6^2[/tex]
First step to solve the above expression is to simplify (5-3) by BODMAS rule then to square the simplification.
Option 3 is correct.
Part C: To choose the expression "five to the third power"
"five to the third power" is
[tex]5^3=5.5.5=125[/tex]
All 3 represents the expression "five to the third power"
Option 1,3,4 are correct.
Part D: The expression -8 · -8 · -8 · -8
The above expression can be written as
[tex](-8)^4[/tex]
Option 2 is correct
Part E: [tex]\text{The value of } -6^2[/tex]
[tex]-6^2=-(6\times 6)=-36[/tex]
Option 1 is correct
Part F: [tex]\text{The value of } |5| - 4(3^2 - 2)[/tex]
[tex]|5| - 4(3^2 - 2)=5-4(9-2)=5-4(7)=5-28=-23[/tex]
Option 4 is correct.
Part G: Evaluate [tex]\frac{8}{ -2}\times 4^2 + 9[/tex]
[tex]\frac{8}{ -2}\times 4^2 + 9=-4\times 16+9=-64+9=-55{ [/tex]
Option 2 is correct.
Part H: Simplify [tex]-5^2 + 8|-1| + (-3)[/tex]
[tex]-5^2 + 8|-1| + (-3)=-25+8-3=-17-3=-20[/tex]
Option 3 is correct.
8x+12=10x-8 help me out bruh
Please helpp!! Due soon
Quadrilateral KLMN is a rectangle. The coordinates of L are L(1,-4), and the coordinates of Mare M(3,-2). Find the slopes of sides KL, LM, MN, and NK.
Answer: its A
Step-by-step explanation: