Answer: 8 3/7
Step-by-step explanation:
32/7 + 3 6/7
= 32/7 + 27/7
= 59/7
= 8 3/7
Hope this helps!
Hello! (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
So you are adding fractions, but not just any fractions, mixed numbers.
So, to start you are gonna wanna turn these mixed numbers into improper fractions.
Here are the steps!
1. Multiply the whole number by the denominator
2. Add that to the numerator
3. Write the number you now have over the original denominator
So 4 4/7 = 32/7
3 6/7 = 27/7
You can only add or subtract fractions with like denominators. This just means denominators with the same number. In our case, we already have like denominators. They are both seven! So the adding process easy. Simply add the numerators and keep the denominators the same!
32 + 27= 59/7
Bam! 59/7 is your answer! If you would like to turn this back into a mixed number, here are the steps:
1. Divide numerator by denominator
2. Put that number as the whole number
3. Use the remainder as the numerator
4. Keep the same denominator
So, 59/7 = 8 3/7
So your answer is 59/7, or, 8 3/7.
Have a great day! And feel free to reply with any questions! (〃^∇^)ﾉ
What is the value of x?
Enter your answer in the box.
Answer:
Since the two angles are across from each other that tells us that they are equal in length, so we want to set them equal to each other
3x+50=6x-10, Now we want to solve it like a normal equation, get x by itself
First add 10 to each side
3x+50+10=6x-10+10
3x+60=6x
Now we want to subtract 3x from each side
3x-3x+60=6x-3x
60=3x
Now divide both sides by 3
60/3=3x/3
20=x
x=20
Hope this helps ;)
Step-by-step explanation:
complete the equation of the line through (-8, 8) and (1, -10)
Answer:
[tex]y=-2x-8[/tex]
Step-by-step explanation:
Let [tex]y=mx+c[/tex] be the equation of this line.
The points must satisfy this equation.
When x=-8, and y=8, we get:
[tex]8=-8m+c....(1)[/tex]
When x=1, and y=-10, we get:
[tex]-10=m+c...(2)[/tex]
Subtract equation (1) from equation (2) to get:
[tex]m--8m=-10-8[/tex]
9m=-18
m=-2
We put m=-2 in equation to get (2)
-10=-2+c
c=-10+2
c=-8
Therefore the equation is:
y=-2x-8
what kind of shape will be this rule on a graph
y= x^2
Answer:
a parabola, sort of like a u shape
Step-by-step explanation:
rachel spent $3.60 for stamps to mail packages. Some were 30-cent stamps and the rest were 20-cent stamps. The number of 20-cent stamps was 2 less than the number of 30-cent stamps. How many stamps of each kind did rachel buy?
Rachel bought six 20-cent stamps and eight 30-cent stamps.
Step-by-step explanation:
Given,
Amount spent on stamps = $3.60 = 3.60*100 = 360 cents
Let,
x = 20 cent stamps
y = 30 cent stamps
According to given statement;
20x+30y=360 Eqn 1
x = y-2 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]20(y-2)+30y=360\\20y-40+30y=360\\50y=360+40\\50y=400[/tex]
Dividing both sides by 50
[tex]\frac{50y}{50}=\frac{400}{50}\\y=8[/tex]
Putting y=8 in Eqn 2
[tex]x=8-2\\x=6[/tex]
Rachel bought six 20-cent stamps and eight 30-cent stamps.
Keywords: linear equation, substitution method
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Final answer:
Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps. We solved a system of equations representing the cost of the stamps and their quantity relationship to determine the numbers.
Explanation:
Rachel spent $3.60 for stamps to mail packages, buying 30-cent stamps and 20-cent stamps. The number of 20-cent stamps was 2 less than the number of 30-cent stamps. To solve this, we can use a system of equations to represent the total cost and the relationship between the number of stamps:
Let x be the number of 30-cent stamps.
Let y be the number of 20-cent stamps.
Based on the information given:
0.30x + 0.20y = 3.60 (Total cost equation)
y = x - 2 (Relationship between the stamps)
We substitute the second equation into the first equation:
0.30x + 0.20(x - 2) = 3.60
0.30x + 0.20x - 0.40 = 3.60
0.50x = 4.00
x = 8
Now we solve for y using the second equation:
y = 8 - 2
y = 6
So Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps.
The measures of the angles of triangle RST are in the ratio 2:4:9. What are the measures of the angles ?
Measures of the angles are 24°, 48° and 108°
Step-by-step explanation:
Step 1: Given ratio = 2:4:9. Sum of angles of triangle = 180°Let angles be 2x, 4x and 9x.
⇒ 2x + 4x + 9x = 180
⇒ 15x = 180
⇒ x = 180/15 = 12
Step 2: Find angles.2x = 24°, 4x = 48° and 9x = 108°
When 15 is subtracted from 3 times a number the result is -32. what is the number?
Answer:
15.6
Step-by-step explanation:
15+32=47
47/3=15.6
since the - is there
it will be -15.6
Answer:
Step-by-step explanation:
let x represent the number
3x - 15 = -32
3x = -32 + 15
3x = -17
x = -17/3 or - 5 2/3 <====
Solve. 5a−12=−2 plzz help
Answer:
a=2
Step-by-step explanation:
Given: 5a-12=-2
Isolate Variable: 5a=10
Divide: a=2
Answer:
5a - 12= -2
5 x 2= 10 so,
5(2) - 12= -2
^
10-12= -2
simplify this,(p-5)^2-49
Answer:
(p - 12)(p + 2) or
p^2 - 10p - 24.
Step-by-step explanation:
We use the Difference of 2 Squares Identity.
a^2 - b^2 = (a - b)(a + b).
So (p - 5)^2 - 49
= (p - 5 - 7)(p - 5 + 7)
= (p - 12)(p + 2)
= p^2 - 10p - 24.
Answer:
(p - 12)(p + 2)
Step-by-step explanation:
(p-5)² - 49 =
= (p - 5 - 7)(p - 5 + 7)
= (p - 12)(p + 2)
a² - b² = (a - b)(a + b)
a = p - 5
b = 49
You start out with $20 and then spend money in a store where every item is $3. Y = -3x + 20.
D
Step-by-step explanation:
The lifespans of tigers in a particular zoo are normally distributed. The average tiger lives 22.4 years; the
standard deviation is 2.7 years.
Use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a tiger living between 27.8 and 30.5
years.
Answer:
[tex] P(27.8 < X <30.5)=P(X>27.8)-P(X>30.5)=0.025-0.0015=0.0235[/tex]
Step-by-step explanation:
The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".
Let X the random variable who represent the lifespans of tigers in a particular zoo.
From the problem we have the mean and the standard deviation for the random variable X. [tex]\mu=120 , \sigma=110[/tex]
On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:
• The probability of obtain values within one deviation from the mean is 0.68
• The probability of obtain values within two deviation's from the mean is 0.95
• The probability of obtain values within three deviation's from the mean is 0.997
We want to find this probability:
[tex] P(27.8 < X <30.5)[/tex]
And in order to calculate how many deviation we are above/below the mean we can use the z score given by:
[tex]z =\frac{x-\mu}{\sigma}[/tex]
And if we use this formula for the two values given we have:
[tex] z_1 = \frac{27.8-22.4}{2.7}=2[/tex]
[tex] z_1 = \frac{30.5-22.4}{2.7}=3[/tex]
So we have values between 2 and 3 deviations above the mean.
We can use the following probabilities
[tex]P(X<\mu -\sigma)=P(X <19.7)=0.16[/tex]
[tex]P(X>\mu +\sigma)=P(X >25.1)=0.16[/tex]
[tex]P(X<\mu -2*\sigma)=P(X<17)=0.025[/tex]
[tex]P(X>\mu +2*\sigma)=P(X>27.8)=0.025[/tex]
[tex]P(X<\mu -3*\sigma)=P(X<14.3)=0.0015[/tex]
[tex]P(X>\mu +3*\sigma)=P(X>30.5)=0.0015[/tex]
And we can find this probability on this way:
[tex] P(27.8 < X <30.5)=P(X>27.8)-P(X>30.5)=0.025-0.0015=0.0235[/tex]
To estimate the probability of a tiger's lifespan falling between 27.8 and 30.5 years, we can use the empirical rule, which states that approximately 95% of the data falls within two standard deviations of the mean.
Explanation:To estimate the probability of a tiger living between 27.8 and 30.5 years, we can use the empirical rule. According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, and approximately 95% falls within two standard deviations. Since the mean is 22.4 years and the standard deviation is 2.7 years, we need to find the probability that a tiger's lifespan falls between 27.8 - 22.4 = 5.4 years and 30.5 - 22.4 = 8.1 years.
Since 5.4 years and 8.1 years are less than two and three standard deviations away from the mean, respectively, the probability can be estimated to be approximately 95% using the empirical rule.
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Function 1: y = 4x + 5 Function 2: The line passing through the points (1, 6) and (3, 10). Which of these functions has the greater rate of change? A) Function 1, because the slope is 5 and the slope of function 2 is 4. B) Function 1, because the slope is 4 and the slope of function 2 is 2. C) Function 2, because the slope is 7 and the slope of function 1 is 5. D) Function 2, because the slope is 5 and the slope of function 1 is 4. Eliminat
Answer:
Step-by-step explanation:
function 1 : y = 4x + 5
In y = mx + b form, which is what ur equation is in, the slope can be found in the m position. So the slope of this function is 4.
function 2 : (1,6),(3,10)
slope = (y2 - y1) / (x2 - x1)
(1,6)...x1 = 1 and y1 = 6
(3,10)...x2 = 3 and y2 = 10
now we sub
slope = (10 - 6) / (3 - 1) = 4/2 = 2
B. Function 1, because the slope is 4 and the slope of function 2 is 2. <==
Answer:
Function 1, because the slope is 4 and the slope of function 2 is 2. Use the slope formula.
3. The Assistant Principal for Curriculum administered a practice SAT test with 50 questions
to students during an after-school tutoring program. She said a score of 30 or above predicts
a good SAT test score. How many students took the test and how many can expect a good
SAT test score?
O
O
A. 28 students took the test and 14 of them can expect a good SAT test score.
B.28 students took the test and 4 of them can expect a good SAT test score.
C. 28 students took the test and 21 of them can expect a good SAT test score.
D. 26 students took the test and 14 of them can expect a good SAT test score.
OO
O Mark for review (Will be highlighted on the review page)
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Answer:
A
Step-by-step explanation:
Answer:
the answer is c
Step-by-step explanation:
Which statements are true? Check all that apply. StartRoot 1.8 EndRoot < 1.8 StartRoot 1.8 EndRoot greater-than 1 StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot 1.3 less-than StartRoot 1.8 EndRoot less-than 1.4 StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2 StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
The first, second, third, and fifth statements are true, but the fourth and sixth statements are false. The responses are based on evaluating the square root calculations.
Explanation:The statements we are analyzing are related to the square root of 1.8 (√1.8). Let's work through them:
√1.8 less than 1.8: This statement is true because the square root of a positive number less than its actual number.√1.8 greater than 1: This is true. Since √1.8 is approximately 1.34, which is greater than 1.√1.8 less than √1.9: This is true. Since the larger the number, the larger its square root will be.1.3 less than √1.8 less than 1.4: This is false. As previously stated, √1.8 is approximately 1.34, so it's not less than 1.3 nor greater than 1.4.√1.9 + √1.8 greater than 2: This is true. √1.9 is approximately 1.38 and √1.8 is 1.34. Adding these values exceeds 2.√1.9 − √1.8 greater than 0.1: This is false. The difference between √1.9 and √1.8 is less than 0.1.Learn more about Square Root Comparisons here:https://brainly.com/question/30877013
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A bag of turf builder sun and shade mix grass seed covers an area of 4000ft.How many bags are needed to cover an area of 35,000ft
Answer: you will get 8.75, but the answer should be 9 bags
Step-by-step explanation:
By what number would you multiply 9/5 to get a product of -1
You should multiply [tex]\frac{9}{5}[/tex] with [tex]\frac{-5}{9}[/tex] to get a product of -1
Solution:
Let the number to be multiplied be "a"
Given that,
By what number would you multiply 9/5 to get a product of -1
'a" multiplied with 9/5 should give a product -1
Therefore, writing it mathematically we get,
[tex]a \times \frac{9}{5} = -1[/tex]
Solve the above equation for "a"
[tex]a \times \frac{9}{5} = -1\\\\a = -1 \times \frac{5}{9}\\\\a = \frac{-5}{9}[/tex]
Therefore, you should multiply [tex]\frac{9}{5}[/tex] with [tex]\frac{-5}{9}[/tex] to get a product of -1
Final answer:
To multiply 9/5 by a number to get -1, you must multiply it by -5/9. This is found by setting up an equation to solve for the unknown number and then isolating the variable on one side of the equation.
Explanation:
To find by what number you would multiply 9/5 to get a product of -1, we can set up an equation that represents this situation:
Let x be the number we are looking for. Then we have the equation: (9/5) × x = -1
To solve for x, we need to divide both sides of the equation by (9/5): x = -1 ÷ (9/5)
Multiplying by the reciprocal of (9/5), which is (5/9), we get:
x = -1 × (5/9)
x = -5/9
Therefore, you must multiply 9/5 by -5/9 to get a product of -1.
Gumballs are 2 for 8 cents. How many gumballs can I buy for 32 cents?
Answer:
8 gumballs.
Step-by-step explanation:
How many cents you have divided by the cost:
32 divided by 8 = 4
The answer times the amount of gumballs:
4 x 2 = 8
8 gumballs.
In the morning, sophie goes to the store the goes to school. In the afternoon she goes from school to her house. The map shows the distance between school and home as 5 cm. If every 4 cm on the scale drawing equals 8 kilometers, how far apart are sophies home and school.
10 km
Step-by-step explanation:
If 4 cm represents 8 kilometers then 1 cm represents;
8 / 4
= 2
1 cm : 2 km
How, then, about 5 cm – the distance between Sophie's home and school?
5 cm : ? km
A cross multiplication;
1 cm : 2 km
5 cm : x km
(5 * 2) = 1 x
x = 10/1
x = 10
(3 tablespoons of butter; 38 Jet-Puffed Marshmallows; and 6 cup of kellogg's rice krispies cereal) yields 12 servings. Janice is an expert at making these treats. For the upcoming Christmas Party, she is expecting 30 people & would like for EVERYONE to get 4 servings EACH. How many of each ingredient will she need?
Answer:
Janice required 30 tablespoons of butter, 380 Jet-Puffed Marshmallows and 60 cup of Kellogg's rice krispies cereal to yield 120 servings.
Step-by-step explanation:
Given that 3 tablespoons of butter, 38 Jet-Puffed Marshmallows, and 6 cup of Kellogg's rice krispies cereal) yields 12 servings.
Now, Janice has to make for 30 people and each with 4 servings for the Christmas Party.
So, there are total (30 × 4) = 120 servings required to make.
So, each and every ingredients of the dish will be required to be made 10 times.
Therefore, Janice required 30 tablespoons of butter, 380 Jet-Puffed Marshmallows and 60 cup of Kellogg's rice krispies cereal to yield 120 servings. (Answer)
Janice will need 30 tablespoons of butter, 380 marshmallows, and 60 cups of rice krispies cereal for the Christmas Party.
Explanation:To find out how many of each ingredient Janice will need, we need to calculate the total servings required for the Christmas Party. She is expecting 30 people and wants everyone to have 4 servings each. So the total servings required would be 30 * 4 = 120 servings.
Now, we can calculate the ratio of servings to each ingredient. If 12 servings require 3 tablespoons of butter, then 120 servings would require (120/12) * 3 = 30 tablespoons of butter.
Similarly, if 12 servings require 38 marshmallows, then 120 servings would require (120/12) * 38 = 380 marshmallows. And if 12 servings require 6 cups of rice krispies cereal, then 120 servings would require (120/12) * 6 = 60 cups of rice krispies cereal.
So, Janice will need 30 tablespoons of butter, 380 marshmallows, and 60 cups of rice krispies cereal for the Christmas Party.
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find the equation of the line shown
Answer:
[tex]y = 2x - 1[/tex]
Step-by-step explanation:
The line shown is a straight line its equation is of the form.
[tex]y = mx + c[/tex]
Where m is the slope and c is the y-intercept.
From the graph, the slope is
[tex]m = \frac{rise}{run} [/tex]
[tex]m = \frac{2}{1} = 2[/tex]
The y-intercept from the graph is where the line intersects the y-axis, so c=-1
We substitute the values to get:
[tex]y = 2x - 1[/tex]
Explanation of how to find the equation of lines based on their slopes and intercepts.
Explanation:Equation of the line: The equation of the left line is y = -x + 1 and the equation of the right line is y = 1/2x - 1/2.
Using Slope-Intercept Form: The slope-intercept form of the equation y = mx + b helps determine the equations of lines based on their slopes and intercepts.
Point-Slope Formula: By using the point-slope formula, which utilizes a point on the line and the line's slope, we can find the equation of a line.
The 1984 movie footloose made $8,556,965 in its opening weekend. The 2011 remake of footloose made $15,556,113 in its opening weekend. What is the absolute and relative change in opening weekend earnings from the original footloose to its remake? Round your answer for relative change to the nearest hundreth of a percent. Do not round until your final answer.
Answer:
absolute change: $6,999,148relative change: 81.79%Step-by-step explanation:
The absolute change is the difference between the earnings numbers:
$15,556,113 -8,556,965 = $6,999,148
__
The relative change is the ratio of this difference to the original amount:
$6,999,148/$8,556,965 × 100% ≈ 81.794748% ≈ 81.79%
The absolute change in opening weekend earnings from the original Footloose to its remake is $6,999,148, and the relative change is approximately 81.74%.
Explanation:To calculate the absolute change in opening weekend earnings from the original Footloose movie to its 2011 remake, we subtract the earnings of the original movie from the earnings of the remake. Thus, the absolute change is $15,556,113 - $8,556,965 = $6,999,148.
To find the relative change, we divide the absolute change by the original amount and then multiply by 100 to get a percentage. This gives us ($6,999,148 / $8,556,965) * 100 ≈ 81.74%. Hence, the relative change is approximately 81.74%.
The absolute change represents the direct increase in dollar amount, while the relative change gives us the percentage increase from the original to the remake's opening weekend earnings, providing insight into the growth rate.
A line intersects the points (14, -3) and (9, -11).
Find the slope of the line and simplify completely.
Slope =
Answer:
8/5 or 1 3/5
Step-by-step explanation:
3x − 14y = –20 what the answer i need help please
Answer:
Boooommm x= -2
Step-by-step explanation:
3x − 14y = –20
ok so 3x-14y=-20
+14 to invert the fraction
-20+14=-6
3x=-6
-6/3=-2
x=-2
Please help
Find the volume for each individual shape
Find the composite volume of the original figure.
Answer:
92.11 cm³
Step-by-step explanation:
The figure below;
Has two hemispheres, and An open cylinder The radius of the hemisphere is 2 mmThe height of the cylinder is 6 mm (10 mm - 4 mm)We are required to determine the volume of the figure;
The volume of a hemisphere is given by;
Volume hemisphere = 2/3πr³
Taking π to be 3.14
The Volume of the two hemisphere;
= 2/3 × 3.14 × 2³
= 16.75 cm³
Volume of the cylinder;
Volume = πr²h
= 3.14 × 2² × 6
= 75.36 cm³
Thus, volume of the figure;
= 16.75 cm³ + 75.36 cm³
= 92.11 cm³
Hence, the volume of the figure is 92.11 cm³
What is
p² + (p +7)²=169
Answer:
-12 or 5
Step-by-step explanation:
p² + (p+7)² = 169
p² + (p²+14p+49) = 169
2p² + 14p + 49 - 169 = 0
2p² + 14p - 120 = 0
2p² + 24p - 10p - 120 = 0
2p(p+12) - 10(p+12) = 0
(p+12)(2p-10) = 0
p+12 = 0 , or 2p-10 = 0
p = -12 or 5
Answer:
p = 3
Step-by-step explanation:
p² + (p +7)²=169
Open the bracket and solve the value in the bracket according to BODMAS
p^2 + p^2 + 7^2 = 13^2
Square Root the both side of the equation.
√{p^2} + √{p^2} + √{7^2} = √{13^2}
p + p +7 = 13
2p + 7 = 13
collect like term of the numbers
2p = 13 - 7
2p = 6
Divide both side by the coefficient of p.
2p/2 = 6/2
p = 3.
Write an equation that represents "eight more than twice a number is fifty".
Answer:
8+2x=50
happy to help!!
Answer the questions
Answer:
I just know that for number 9.)It's C because it has a greater number, meaning it has a greater chance of containing Adam's house number.
start time 7:30am elapsed time 2hour,20 minutes end time
Answer:
End time = 9:50
Step-by-step explanation:
Elapsed time = End time - start time
End time = Elapsed time + start time
End time = 2 hour,20 minutes + 7:30
End time = 9:50
What is the area Of a circle that has a circumference of 10 pi.
Answer:
circumference = 10 pi = 2r pi
then r =5
next area of circle = 5 .5.pi = 25 pi
Step-by-step explanation:
Hector Drew three rectangles to show the letter H on his notebook use the rectangles to find the area of the letter he drew
Answer:
Step-by-step explanation:
The area of the H is 86
Answer: Just draw a line at the end of each
Step-by-step explanation: Like this
H I I at the end
you earned 139.20 in simple interest off of 1450 investment in 8 years. What is your annual percentage rate?(Expressed as a percent)
The annual percentage rate is: 1.2%
Step-by-step explanation:
The formula for calculating simple interest is:
[tex]I = Prt[/tex]
Here
P is the principal amount
r is the interest rate
t is the time in years
We are Given:
[tex]P = 1450\\t = 8\ years\\I = 139.20[/tex]
Putting the values in the formula
[tex]139.20 = 1450 * r * 8\\139.20 = 11600r[/tex]
Dividing both sides by 11600
[tex]\frac{11600r}{11600} = \frac{139.20}{11600}\\r = 0.012[/tex]
Converting into percentage
r = 0.012*100
r = 1.2%
Hence,
The annual percentage rate is: 1.2%
Keywords: Percentage, interest
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