13. Puppies have 28 teeth and most adult dogs have 42 teeth. Find the primefactorization of each number. Write the result using exponents. (Example 5)
Answers
To solve our question, first we need to know that a prime factorization is a way to represent a number by a sequence of prime numbers that multiplied together gives us the original number.
So let's calculate our first prime factorization:
As we can see, we divide our number by the smallest prime number and then the factor we follow the same rule until we get "1" (for all divisions we just have integers).
Now, for the second number we have:
And both prime factorizations are our final answers.
Related Questions
Martin earns $7.50 per hour proofreading ads per hour proofreading ads at a local newspaper. His weekly wage can. e found by multiplying his salary times the number of hours h he works.1. Write an equation.2. Find f(15)3. Find f (25)
Answers
If Martin earns 7.50 per hour (that is h), then the equation for his weekly wage can be expressed as;
[tex]\begin{gathered} (A)f(h)=7.5h \\ (B)f(15)=7.5(15) \\ f(15)=112.5 \\ (C)f(25)=7.5(25) \\ f(25)=187.5 \end{gathered}[/tex]Therefore, answer number A shows the equation for his salary
Answer number 2 shows his salary at 15 hours ($112.5)
Answer number 3 shows his salary at 25 hours ($187.5)
During a game, 65% of the pitches Tina threw were strikes. She threw 120 2 poi total pitches during the game. How many throws were strikes? * a) 92 O b) 65 c) 78 d) 44
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how do I find the perimeter of a quadrilateral on a graph?
Answers
The perimeter of a figure is always the sum of the lengths of the sides.
If we have the coordinates of the vertices of the quadrilateral, we can calculate the length of each side as the distance between the vertices.
For example, the length of a side AB will be the distance between the points A and B:
[tex]d=\sqrt[]{(x_b-x_a)^2+\mleft(y_b-y_a\mright)^2}[/tex]Adding the length of the four sides will give the perimeter of the quadrilateral.
a. find a length of segment DF . use decimal rotation _______ unitsb. find the length of segment DF. use decimal rotation _______ units
Answers
write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the equation(-3, -5); y = -5x+2
Answers
The equation is y = -5x-20.
GIven:
The equation is, y = -5x + 2.
A point on the line is (-3, 5).
The objective is to write an equation that passes throught the point and parallel to the given equation.
For parallel lines the product of slope values will be equal.
From the given equation, consider the slope of the equation as, m1 = -5.
Then, the slope of the parallel line will also be, m2 = -5.
Then, the equation of parallel line can be written as,
[tex]\begin{gathered} y=m_2x+b \\ y=-5x+b \end{gathered}[/tex]Here b represents the y intercept of the parellel line.
To find the value of b, substitute the given points in the above equation.
[tex]\begin{gathered} -5=-5(-3)+b \\ -5=15+b \\ b=-5-15 \\ b=-20 \end{gathered}[/tex]Now, substitute the value of b in the equation of parellel line.
[tex]y=-5x-20[/tex]Hence, the equation of parellel line is y = -5x-20.
Write the equation of a line that is parallel to y = 1/2x -4 and that passes through the point (9, -6)
Answers
The most appropriate choice for equation of line in slope intercept form will be given by-
[tex]y = \frac{1}{2}x - \frac{21}{2}[/tex] is the required equation of line
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by [tex]y = mx + c[/tex]
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line
Here,
The given equation of line is [tex]y = \frac{1}{2} x - 4[/tex]
Slope of this line = [tex]\frac{1}{2}[/tex]
Slope of the line parallel to this line = [tex]\frac{1}{2}[/tex]
The line passes through (9 , -6)
Equation of the required line =
[tex]y - (-6) = \frac{1}{2}(x - 9)\\2y + 12 = x - 9\\2y = x - 9 -12\\2y = x -21\\y = \frac{1}{2}x - \frac{21}{2}[/tex]
To learn more about equation of line in slope intercept form, refer to the link-
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If the inflation has been 2.7%, how much more do you have to pay this year foran item that cost $11.50 last year?
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Given data:
The cost of the item is $11.50.
The inflation percentage is 2.7%.
Increase in the price is,
[tex]\begin{gathered} =11.50\times(\frac{2.7}{100}_{}) \\ =11.50\times0.027 \\ =0.3105 \end{gathered}[/tex]Total amount to be paid last year,
[tex]\begin{gathered} =11.50+0.3105 \\ =11.8105 \end{gathered}[/tex]Therefore you will have to pay $ 0.3105 more.
Write 0.000000000054 in scientific notation
Answers
Answer:
5.4 × 10^-11
Step-by-step explanation:
Shawn needs to reach a windowsill that is 10 feet above the ground. He placed his ladder 4 feet from the base of the wall. It reached the base of the window.
a. Draw a diagram of the right triangle formed by Shawn's ladder, the ground and the wall.
b. Find the length of Shawn's ladder to the nearest tenth of a foot.
Answers
If shown needs to reach a windowsill that is 10 feet above the ground and he placed his ladder 4 feet from the base of the wall.
Part a
The diagram of the right triangle formed by Shawn's ladder, the ground and wall has been plotted
Part b
The length of the Shawn's ladder is 10 foot
The distance between ladder base to the base of the wall = 4 feet
The distance between the wall base to the base of the window = 10 feet
Draw the right triangle using the given details
Part b
Using the Pythagorean theorem
[tex]AC^2= AB^2+BC^2[/tex]
Where AC is the length of the ladder
Substitute the values in the equation
AC = [tex]\sqrt{10^2+4^2}[/tex]
= [tex]\sqrt{100+16}[/tex]
= [tex]\sqrt{116}[/tex]
= 10.77
≈ 10 Foot
Hence, if shown needs to reach a windowsill that is 10 feet above the ground and he placed his ladder 4 feet from the base of the wall.
Part a
The diagram of the right triangle formed by Shawn's ladder, the ground and wall has been plotted
Part b
The length of the Shawn's ladder is 10 foot
Learn more about Pythagorean theorem here
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A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.Grocery OptionsStoreOnlineTotalWomen231235Men221537Total452772What percent of the people surveyed shop at a local grocery store? Round your answer to the nearest whole number percent
Answers
Given:
A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online. Grocery Options
Store Online Total
Women 23 12 35
Men 22 15 37
Total 45 27 72
Required:
To find the percentage of the people surveyed shop at a local grocery store.
Explanation:
The total number of people is 75.
And the total number of people surveyed shop at a local grocery store is 45.
Now the percentage of the people surveyed shop at a local grocery store is,
[tex]=\frac{45}{72}\times100[/tex][tex]\begin{gathered} =62.5\% \\ \\ \approx63\% \end{gathered}[/tex]Final Answer:
63% of the people surveyed shop at a local grocery store.
Rosa receives money from her relatives every year on her birthday. Last year, she received a total of $350. This year, she received $441. What is the percent of increase in Rosa’s annual birthday money?
Answers
Answer:
26%
Step-by-step explanation:
use a online percentage calculator
Simplify the following equations in ax^2+bx+c=0 or ay^2+c=0 2x+y=6 4x^2+5y+y+1=0
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Given the equation;
[tex]4x^2+5y^2+y+1=0[/tex]We shall begin by Subtracting 5y^2 + y from both sides;
[tex]\begin{gathered} 4x^2+5y^2+y+1-5y^2-y=0-5y^2-y \\ 4x^2+1=-5y^2-y \\ \text{Factor out -1 from the right hand side;} \\ 4x^2+1=-1(5y^2+y) \end{gathered}[/tex]Next step we subtract 1 from both sides;
[tex]\begin{gathered} 4x^2+1-1=-1(5y^2+y)-1 \\ 4x^2=-(5y^2+y)-1 \\ \end{gathered}[/tex]Next step we take the square root of both sides;
[tex]\begin{gathered} \sqrt[]{4x^2}=\pm\sqrt[]{-(5y^2+y)-1} \\ 2x=\pm\sqrt[]{-(5y^2+y)-1} \end{gathered}[/tex]We can now open the parenthesis on the right hand side;
[tex]\begin{gathered} 2x=\pm\sqrt[]{-5y^2-y-1} \\ \text{Divide both sides by 2;} \\ x=\frac{\pm\sqrt[]{-5y^2-y-1}}{2} \end{gathered}[/tex][tex]undefined[/tex]The shorter leg of a right triangle is 9cm shorter than the longer leg. The hypotenuse is 9cm longer than the longer leg. Find the side lengths of the triangle.Length of the shorter leg: _ cmLength of the longer leg:__ cmLength of hypotenuse __ cm
Answers
Explanation:
let the longer leg = x
The shorter leg = 9cm shorter than the longer leg
The shorter leg = x - 9
hypotenuse = 9cm longer than the longer leg
hypotenuse = x + 9
Using pythagoras theorem:
hypotenuse² = shorter leg² + longer leg²
(x + 9)² = x² + (x - 9)²
Expanding:
x² + 9x + 9x + 81 = x² + x ² - 9x -9x + 81
x² + 18x + 81 = 2x² -18x + 81
collect like terms:
18x + 18x + 81 - 81 = 2x² - x²
36x + 0 = x²
x² - 36x = 0
x(x - 36) = 0
x = 0 or (x - 36) = 0
x = 0 or x = 36
if x = 0
shorter side = x - 9 = 0 - 9 = -9
Since the length cannot be negative, x = 36
The longer leg = x = 36 cm
The shorter leg = x - 9 = 36 - 9
The shorter leg = 27cm
The hypotenuse = x + 9 = 36 + 9
The hypotenuse = 45 cm
If students only know the radius of a circle, what other measures could they determine? Explain how students would use the radius to find the other parts.
Answers
Radius of the circle : Radius is the distance from the center outwards.
With the help of radius we can determine the following terms:
1. Diameter : Diameter is the twice of radius and it is teh staright line that passes through the center. Expression for the diameter is :
[tex]\text{ Diameter= 2}\times Radius[/tex]2. Circumference: Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. It express as:
[tex]\begin{gathered} \text{ Circumference of Circle=2}\Pi(Radius) \\ \text{ where }\Pi=3.14 \end{gathered}[/tex]3. Area of Circle: Area of a circle is the region occupied by the circle in a two-dimensional plane. It express as:
[tex]\begin{gathered} \text{ Area of Circle = }\Pi(radius)^2 \\ \text{where : }\Pi=3.14 \end{gathered}[/tex]4. Center Angle of the Sector: Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one. It express as :
[tex]\text{ Central Angle of sector=}\frac{Area\text{ of Sector}}{\Pi(radius)^2}\times360[/tex]5. Arc length : An arc of a circle is any portion of the circumference of a circle. It express as :
[tex]\text{ Arc Length = }Radius(\text{ Angle Substended by the arc from the centerof crircle)}[/tex]In the given figure the radius is AO & BO
write the following comparison as a ratio reduced to lowest terms. 21 quarters to 13 dollars
Answers
In order to calculate the ratio of these values, let's divide them, using the fraction form:
[tex]\text{ratio}=\frac{21}{13}[/tex]Since the numbers 21 and 13 don't have any common factor, the fraction is already in the lowest terms.
So the ratio is 21:13
9. The Elite Vacuum Company has determined its cost for making vacuums to beC = 24V + 1000, where C is the cost in dollars and V is the number of vacuums.If the cost must be between $49,000 and $121,000, how many vacuums can they makeper week? (You must set up and solve an inequality.)
Answers
We are given the relationship between the cost in dollars (C) and the number of vacuums (V) to be:
[tex]C\text{ = 24V + 1000}[/tex]From the constraint, we have that the cost(C) must be greater than $49000 and less than $121000
Writing this as inequality:
[tex]\begin{gathered} 24V\text{ + 1000 }\ge\text{ 49000 } \\ 24V\text{ + 1000 }\leq\text{ 121000} \end{gathered}[/tex]Solving the linear inequalities for V:
[tex]\begin{gathered} 24V\text{ + 1000 }\ge\text{ 49000} \\ 24V\text{ }\ge\text{ 49000 - 1000} \\ 24V\text{ }\ge\text{ 48000} \\ \text{Divide both sides by 24} \\ \frac{24V}{24}\text{ }\ge\text{ }\frac{48000}{24} \\ V\text{ }\ge\text{ 2000} \end{gathered}[/tex]Similarly for the second inequality:
[tex]\begin{gathered} 24V\text{ + 1000 }\leq\text{ 121000} \\ 24V\text{ }\leq121000\text{ - 1000} \\ 24V\text{ }\leq\text{ 120000} \\ \text{Divide both sides by 24} \\ \frac{24V}{24}\text{ }\leq\text{ }\frac{120000}{24} \\ V\text{ }\leq5000 \end{gathered}[/tex]Hence, the number of vacuums they can make per week can be between 2000 and 5000 or in inequality:
[tex]2000\text{ }\leq\text{ V }\leq\text{ 5000}[/tex]Answer:
Between 2000 and 5000 vacuums
Question 10 of 11 Step 1 of 1CorrectThcorrectOne group (A) contains 390 people. Three fifths of the people in group A will be selected to win $100 fuel cards. There is another group (B) in a nearby town that willreceive the same number of fuel cards, but there are 553 people in that group. What will be the ratio of nonwinners in group Ato nonwinners in group B after theselections are made? Express your ratio as a fraction or with a colon.AnswerkeypadRestore Your Guth2019 Hawkes Learning
Answers
Given : Two groups
Group A: contains 390 people.
Three fifths of the people in group A will be selected to win $100 fuel cards.
So, the number of people who will win = 3/5 * 390 = 234
Group B : contains 553 people
the group will receive the same number of fuel cards
so, the group will receive 234 cards
The non-winners of group A = 390 - 234 = 156
The non-winners of group B = 553 - 234 = 319
The ratio between them = 156 : 319
Maya bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $400 less than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was 7.5 % per year and for the laptop it was 8% per year. The total finance charges for one year were $371. How much did each computer cost before finance charges? Desktop: $Laptop: $
Answers
1. Let D be price of desktop
let L be price of a Laptop
• we know that the laptop cost $400 less than the desktop
L = D -400
• for desktop D, Maya paid interest of 7.5% per year: 7.5/100 = 0.075
,• For Laptop L , Maya paid interest of 8 % per year : 8/100 = 0.08
,• We know that total charges for finance was $ 371,
therefore :
0.075 D + 0.08L = 371, (remember from the above , L = D-400 , lets substitute this value for L)
0.075 D + 0.08( D-400) = 371
0.075D + 0.08 D -32 = 371
0.155D = (371 +32)=403
D = 403/0.0155
D = $26 000
and L = D-400
= 26000-400
= $25600
• This means that Desktopcost $26000 and Laptop cost $25600,
Saltarecis a maker of high-end apparel for woman. For market research one afternoon, Saltare’s sales team surveyed adult women at a busy airport on the number of blouses they own. The histogram below summarizes the data. Use the histogram to answer each of the questions
Answers
(a)
The class width of the histogram is given by the range of each bar in the histogram, that is, the upper limit minus the lower limit of a bar (plus 1, since we need to include the boundary values of the range).
Looking at the first bar, the upper limit is 19 and the lower limit is 11, therefore the class width is 9 (because there are 9 elements between 11 and 19, so we need to add 1 to the subtraction of 19 and 11)
(b)
The most frequent class is the third one (third vertical bar).
The frequency of this bar (that is, the value in the y-axis) is equal to 8.
Therefore 8 women are in this class.
(c)
The number of women with 28 or fewer blouses is given by the frequency of the first two bars.
Adding the frequency of the first bar (1) and the frequency of the second bar (5), we have that 6 women have 28 or fewer blouses.
8% of the students at Jemerson Middle School are absent because of illness. If there are 150 students in the school, how many are absent? 12015128
Answers
12 students
Explanation
when you have 8% , it means 8 of every 100 students are absent
find the decimal form
[tex]8\text{ \% = }\frac{8}{100}=0.08[/tex]then, to find the 8% of any number, just multiply the number by 0.08
Step 1
If there are 150 students in the school, how many are absent?
[tex]\begin{gathered} \text{absent}=\text{total}\cdot0.08 \\ \text{absent}=150\cdot0.08 \\ \text{absent}=12 \end{gathered}[/tex]so, 12 students are absent
the first yr a community college offered a Certificate in data management , 12 people earned the certificate. the next year 17 people earned the certificate. what was the percent increase in the # of people earning the certificate?
Answers
we make an expression
[tex]12\times x=17[/tex]we know that if we multiply to twelve by the ratio of increase we will obtain 17
now solve for x that is the ratio
[tex]x=\frac{17}{12}=1.42[/tex]multiply by 100 to obtain a percentage
[tex]1.42\times100=142[/tex]the percentage is 142%
As you landscape a 4 leaf clover intersection, you will need to buy enough grass seed to cover all 4 circies. Each of the circles has the same diameter: 41 meters. Calculate the total area of all grass seed needed to cover all 4 circles.
Answers
SOLUTION
Each of the circles has the same diameter: 41 meters.
If the diameter = 41 meters
Then the Radius =
[tex]\frac{41}{2}\text{ m}[/tex]Then we need to find the total area of the 4 circles =
[tex]\begin{gathered} 4\text{ X }\pi r^2 \\ =\text{ 4 X }\frac{22}{7\text{ }}\text{ X }\frac{41}{2}\text{ X}\frac{41}{2} \\ =\text{ }5283\text{ }\frac{1}{7}m^2 \end{gathered}[/tex]CONCLUSION: The total area of all grass seeds needed to cover all 4 circles =
[tex]5283\text{ }\frac{1}{7}m^2[/tex]
Find the perimeter of the rectangle. Write your answer in scientific notation.Area = 5.612 times 10^14 cm squared9.2 times 10^7cm is one side of the perimeter
Answers
Answer: Perimeter = 1.962 x 10^8 cm
Explanation:
The first step is to calculate the width of the rectangle. Recall,
Area = length x width
width = Area /length
From the information given,
Area = 5.612 times 10^14 cm squared
Length = 9.2 times 10^7cm
Thus,
width = 5.612 times 10^14 /9.2 times 10^7
width = 6.1 x 10^6
The formula for calculating the perimeter is
Perimeter = 2(length + width)
Thus,
Perimeter = 2(9.2 x 10^7 + 6.1 x 10^6)
Perimeter = 1.962 x 10^8 cm
need help, what's the answer for the x and y?
Answers
Line equation in slope and y-intercept form:
y = mx + b
To calculate the slope, we use the first two points: (24,-15) and (28, -17)
m = (y2 - y1)/(x2 - x1)
m = (-17 - (-15))/(28 - 24)
m = (-17 + 15)/(4
m = -2/4 = -1/2
To find b we use the first point: (24, -15)
y = mx + b
b = y - mx = -15 - (-1/2)(24) = -15 + 12 = -3
b = -3
Answer:
y = (-1/2) x - 3
Lucky's Market purchased a new freezer for the store.When the freezer door stays open, the temperatureinside rises. The table shows how much thetemperature rises every 15 minutes. Find the unit rate.temperature (°F) =10number of minutes =15(answer) °F per minute
Answers
Notice that the information in the table can be modeled using a linear function. To find the slope (rate of change) given two points, use the formula below
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow slope=m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (15,10),(30,20) \\ \Rightarrow slope=\frac{20-10}{30-15}=\frac{10}{15}=\frac{2}{3} \end{gathered}[/tex]Can u please help me solve ? I'm reviewing for a final, ty
Answers
Part A
we have that
Both students verify the identity properly
student A ----> expand the left side of the identity
student B ----> expand the right side of the identity
but the result is the same
both students proved that the given equation is an identity
Part B
Identities[tex]\begin{gathered} sin^2x+cos^2x=1\text{ ----> identity N 1 in step 3} \\ cos^2x=1-sin^2x \end{gathered}[/tex]and
[tex]cscx=\frac{1}{sinx}\text{ -----> identity N 2 step 5}[/tex]Slove for p 14 = -(p - 8)
Answers
Solve:
[tex]\begin{gathered} 14=-(p-8) \\ -14=p-8 \\ -14+8=p \\ p=-14+8 \\ p=-6 \end{gathered}[/tex]p=-6
Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this section to solve the following exercise.A shirt and a tie together cost $68. The shirt costs $30 more than the tie. What is the cost of the shirt (in dollars).
Answers
Let x and y be the cost of a shirt and a tie, respectively; therefore, the two equations are
[tex]\begin{gathered} x+y=68 \\ \text{and} \\ x=30+y \end{gathered}[/tex]We have two variables and two equations; we need to solve the system of equations to find the values of x and y.
Solve using the substitution method.
Use the second equation into the first equation, as shown below
[tex]\begin{gathered} x=30+y \\ \Rightarrow(30+y)+y=68 \\ \Rightarrow30+2y=68 \\ \Rightarrow2y=68-30=38 \\ \Rightarrow y=\frac{38}{2} \\ \Rightarrow y=19 \end{gathered}[/tex]Now, use this value of y in the second equation
[tex]\begin{gathered} y=19 \\ \Rightarrow x=30+y=30+19 \\ \Rightarrow x=49 \end{gathered}[/tex]Remember that x is the cost of a shirt and y is the cost of a tie. Therefore, the answers are
Cost of a shirt: $49
Cost of a tie: $19
One can verify the answer by noticing that a shirt and a tie cost $49+$19=$68, and that a shirt costs $30+$19=$49
Solve this system of equations by substitution. Enter your answer as an ordered pair (x,y). Do not use spaces in your answer.
Answers
We have the following:
[tex]\begin{gathered} y=-\frac{1}{2}x+4 \\ y=2x-1 \end{gathered}[/tex]Solving by substitution
[tex]\begin{gathered} -\frac{1}{2}x+4=2x-1 \\ 2x+\frac{1}{2}x=4+1 \\ \frac{5}{2}x=5 \\ x=\frac{2\cdot5}{5} \\ x=2 \end{gathered}[/tex]Now for y
[tex]\begin{gathered} y=2\cdot2-1=4-1=3 \\ \end{gathered}[/tex]Therefore, the answer is:
[tex](2,3)[/tex]Write an expression for the sequence of operations described below.1)) multiply 7 by 8, then divide f by the resultDo not simplify any part of the expression.Submit
Answers
We need to write an expression for the operations:
[tex]\begin{gathered} \text{ multiply 7 by 8} \\ \\ \text{dived f by the result} \end{gathered}[/tex]The first operation (multiplication) can be represented as:
[tex]7\cdot8[/tex]The second operation (the division of f by the previous result) can be represented as:
[tex]f\div(7\cdot8)[/tex]Notice that we need the parenthesis to indicate that the product is the first operation to be done.
Answer:
[tex]f\div(7\cdot8)[/tex]