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
Study the diagram, where AB and C'D are chords that intersect inside of the circle at point P, which is not the center.
Answers
Answer:
answer of the given question
A triangular road sign has a base of 30 inches and a height of 40 inches. What is it’s area?
Answers
Answer:
600ft
Step-by-step explanation:
Because a triangle is half of a rectangle, the area can be found by taking the base times height and dividing by 2.
A = (b * h)/2
A = (40 * 30)/2
A = 1200/2
A = 600ft
D is the midpoint of AC, BA ≅BC and ∠EDA ≅ ∠FDC. Prove ΔAED ≅ ΔCFD
Answers
We are asked to prove that triangles AED and CFD are congruent. To do that we will prove that we can use the ASA (Angle Side Angle) rule of congruency.
First, we are given that D is a midpoint of segment AC, therefore:
[tex]\bar{AD}=\bar{AC}[/tex]Also, we are given that:
[tex]\bar{BA}=\bar{BC}[/tex]This means that triangle ABC is an isosceles triangle and therefore, its base angles are equal. This means that:
[tex]\angle BAC=\angle BCA[/tex]And, since we are given that angles EDA and FDC are equal, then by ASA we can conclude that:
[tex]\Delta AED\cong\Delta CFD[/tex]Suppose elephant poaching reduces an initial animal population of 25,000 animals by 15% each year. 1. Find the rate of change.2. How many animals will be left in 10 years?
Answers
Answer
Initial animal population, P₀ = 25,000
1. Rate of change = 15% = 0.15
2. Animal left in 10 years?
To calculate the animals left in 10 years, we use the formula:
P(t) = P₀ (1 - r)^t in t years
t = 10, P₀ = 25,000, r = 15% = 0.15)
P₍₁₀₎ = 25000 (1 - 0.15)¹⁰
P₍₁₀₎ = 25000 (0.85)¹⁰
P₍₁₀₎ = 25000 (0.1969)
P₍₁₀₎ = 4922.50
Therefore, 4922.50 animals will be left in 10 years.
Solve the following equations. (You may leave your answer in terms of logarithms or you can plug your answer into a calculator to get a decimal approximation.)
Answers
Given the equation:
[tex]200(1.06)^t=550[/tex]We divide each side by 200:
[tex]\begin{gathered} \frac{200}{200}(1.06)^t=\frac{550}{200} \\ 1.06^t=2.75 \end{gathered}[/tex]Now, we take the natural logarithm:
[tex]\begin{gathered} \ln (1.06^t)=\ln (2.75) \\ t\cdot\ln (1.06)=\ln (2.75) \\ \therefore t=\frac{\ln (2.75)}{\ln (1.06)} \end{gathered}[/tex]A park meadow is planted with wildflowers. The Parks Department plans to extend the length of the rectangular meadow by x meters. Which expressions represent the total area, in square meters, after the meadow's length is increased? Select all that apply. 15. A 310 + x B 15.5(20x) C 20x + 15.5 D 15.5x + 310 E 15.5(20 + x) F 35.5 + x Ilse the distributi
Answers
We have the following:
The area would be the length by the width, but since x amount was added to the length, it would be like this
[tex]\begin{gathered} A=w\cdot l \\ w=15.5 \\ l=20+x \end{gathered}[/tex]replacing
[tex]A=15.5\cdot(20+x)=310+15.5x[/tex]Therefore, the answer is E and D
9) The temperature outside feels like - 3°C on Thursday. When the temperature is taken, it is actually 16°C. Howmany degrees lower does the temperature feel?
Answers
The temperature feels
[tex]16-(-3)=19[/tex]degrees lower from the actual.
Given the focus and directrix shown on the graph, what is the vertex form of the equation of the parabola?
[tex]x\ =\ \frac{1}{10}(y\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
[tex]x\ =\ 10(y\ +\ 3)^2\ +\ \frac{3}{2}[/tex]
[tex]x\ =\ \textrm{-}\frac{1}{10}(y\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
[tex]y\ =\ \frac{1}{10}(x\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
Answers
The vertex-form equation of the parabola is given as follows:
y = 1/10(y - 3)² - 3/2.
What is the equation of a horizontal parabola?An horizontal parabola of vertex (h,k) is modeled as follows:
x = (1/4p)(y - k)² + h.
In which:
The directrix is x = h - p.The focus is (h + p, k).In the context of this problem, we have that:
The directrix is x = -4.The focus is: (1,3), hence k = 3.A system of equations is built for h and p as follows:
h - p = -4.h + p = 1.Hence:
2h = -3
h = -3/2.
p = 1 + 3/2 = 2.5.
Then the equation is:
y = 1/10(y - 3)² - 3/2. (first option).
Missing informationThe graph is given by the image at the end of the answer.
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
#SPJ1
An athlete runs at a speed of 9 miles per hour. If one lap is 349 yards, how many laps does he run in 22 minutes
Answers
The athlete will cover 17 yards in 22 minutes of his running.
What is unitary method?The unitary method is a method in which you find the value of a single unit and then the value of a required number of units.
Given is an athlete who runs at a speed of 9 miles per hour and one lap is 349 yards.
We will use the unit conversions to solve the given problem.
The speed of the athlete is 9 mph. We can write it as -
9 mph = (9 x 1760) yards per hour = 15840 yards per hour.
15840 yards per hour = (15840/60) yards per minute = 264 yards per min.
Total yards covered in 22 minutes = 22 x 264 = 5808 yards
one lap is equivalent to 349 yards.
1 yard is equivalent to (1/349) laps
5808 yards are equivalent to (5808/349) or 16.6 yards or approximately 17 yards.
Therefore, the athlete will cover 17 yards in 22 minutes of his running.
To solve more questions on unitary method, visit the link below-
https://brainly.com/question/13659834
#SPJ1
good night I will send a picture of work
Answers
In the form of the equation
S = m D + b
S represented on the y-axis
D represented on the x-axis
The independent is x
The dependent is y
Then D is the independent
S is the dependent
let us find the correct answer
Are the answers to question six part a b c and d correct?
Answers
When you are on the 2nd step of factoring this trinomial,you should be listing the factors of?
Answers
Given:
The trinomial equation is given as,
[tex]3v^2-4v-7[/tex]The objective is to choose the correct value for which the factors are to be obtained for factorization.
Explanation:
From the step 1, to perform the factorization the values of a and c has to be multiplied.
Then in step 2, the factors need to be calculated for the product of a and c.
Product of a and c :
The product of a and c will be,
[tex]a\times c=3\times7=21[/tex]Thus, factors are to be listed for the number 21.
Hence, option (1) is the correct answer.
The width of a rectangle measures (8u - 2v) centimeters, and its length meas(5u +9v) centimeters. Which expression represents the perimeter, in centimof the rectangle?
Answers
The perimeter of a rectangle is given by two times the length plus two times the width, so we have:
[tex]\begin{gathered} P=2L+2W\\ \\ P=2(5u+9v)+2(8u-2v)\\ \\ P=10u+18v+16u-4v\\ \\ P=26u+14v \end{gathered}[/tex]Therefore the perimeter's expression is 26u + 14v
In circle D with the measure of minor aré CE = 162 degrees, find m of CFE
Answers
SOLUTION
Step 1: Make a more comprehensive sketch of the question.
The measure of CFE is 81 degrees.
Can you please help me with 44Please use all 3 forms such as :up/down, as_,_ and limits
Answers
Given:
[tex]h(x)=(x-1)^3(x+3)^2[/tex]The x-intercepts of the given polynomial are
[tex]x-\text{intercepts }=1\text{ (multiplicity 3) and -3 (multiplicity 2)}[/tex]Substitute x=0 in h(x) to find y-intercepts.
[tex]\text{ y-intercepts =}(-1)^3(3)^2=-9[/tex][tex]\lim _{x\to-\infty}h(x)=\lim _{x\to-\infty}(x-1)^3(x+3)^2=-\infty[/tex][tex]as\text{ x}\rightarrow-\infty,\text{ h(x)}\rightarrow-\infty[/tex][tex]\lim _{x\to\infty}h(x)=\lim _{x\to\infty}(x-1)^3(x+3)^2=\infty[/tex][tex]as\text{ x}\rightarrow\infty,\text{ h(x)}\rightarrow\infty[/tex]The graph of the given polynomial h(x) is
The degree of the polynomial is 6=even and the leading coefficient=1=positive.
Both ends of the graph point up.
End behaviour is
up/up.
Find f(-4) and f(3) for the following funxripnf(x)=3x
Answers
Given the function:
[tex]f(x)=3x[/tex]• You need to substitute this value of "x" into the function:
[tex]x=-4[/tex]And then evaluate, in order to find:
[tex]f(-4)[/tex]You get:
[tex]f(-4)=3(-4)[/tex][tex]f(-4)=-12[/tex]Remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]• Substitute this value of "x" into the function:
[tex]x=3[/tex]Then:
[tex]f(3)=3(3)[/tex]Evaluate, in order to find:
[tex]f(3)[/tex]You get:
[tex]f(3)=9[/tex]Hence, the answer is:
[tex]\begin{gathered} f(-4)=-12 \\ f(3)=9 \end{gathered}[/tex]Subway wants to know how their customers feel about their food quality and service. When each customer pays for their food, the Subway employee hands them their receipt and tells them that they have a chance to win $500 if they go on line and answer a few questions about the restaurant. a) Experimentb) Observational Studyc) None of thesed) Survey
Answers
From the question, we were told that a subway company decides to reward their customers if they go online and answer a few questions about the restaurant.
We are to determine what the process means.
The general view, examination, or description of something or someone in most cases for a reward is known as a survey.
So since subway wants its customers to go online and answer some question about the restaurant and get a reward, then it is a survey.
So, the process that was carried out is a survey.
Therefore, the correct option is D, which is survey.
A graph has age (weeks) on the x-axis, and height (inches) on the y-axis. Points are grouped closely together. One point is outside of the cluster. Which statement is true? There is no relationship between the height of the plant and its age. Although the outlier is an extreme value, it should be included in the interpretation. By excluding the outlier, a better description can be given for the data set
Answers
Answer:
Step-by-step explanation:
The answer is C
Answer:All three 1. to compare groups, not individuals2. to lessen the influence of outliers3. to clearly see trends
Explanation:edge 2022
Draw a figure to use for numbers 13 - 15. Points A. B. and C are collinear and Bis the midpoint of AC. 13. If AB = 3x - 8 and BC = x + 4, find the length of AB 14. If BC = 6x - 7 and AB = 5x + 1. find the length of AC 15. If AB = 8x + 11 and BC = 12x - 1. find the length of BCAnswer 13
Answers
13.
Given:
AB = 3x - 8, BC = x + 4
A, B and C are collinear
B is a midpoint of AC
Since B is the midpoint, we can write:
[tex]\text{length of AB = Length of BC}[/tex]Hence, we have:
[tex]3x\text{ - 8 = x + 4}[/tex]Solving for x:
[tex]\begin{gathered} \text{Collect like terms} \\ 3x\text{ -x = 4 + 8} \\ 2x\text{ = 12} \\ \text{Divide both sides by 2} \\ x\text{ = 6} \end{gathered}[/tex]Hence, the length of AB is:
[tex]\begin{gathered} =\text{ 3x - 8} \\ =\text{ 3}\times\text{ 6 -8} \\ =\text{ 18 -8} \\ =\text{ 10} \end{gathered}[/tex]Answer:
The length of AB is 10 unit
How does basic algebra come to play in everyday life? Explain (or give examples) in at least two sentences
Answers
Explanation
1) Algebra can be used while cooking to estimate the amount of ingredients by solving some easy algebraic expressions of the head.
e.g 2 tea spoons of pepper out of a 1kg pack might be the right amount to spice a soup.
2) For example, a plumber may do some quick calculations to determine the number of pipes required for a house
e.g 5 pipes in the bathroom, two pipes in the toilet, three in the kitchen gives 10 pipes altogether.
A forest products company claims that the amount of usable lumber in its harvested trees averages142 cubic feet and has a standard deviation of 9 cubic feet. Assume that these amounts haveapproximately a normal distribution.1. What percent of the trees contain between 133 and 169 cubic feet of lumber? Round to twodecimal places.II. If 18,000 trees are usable, how many trees yield more than 151 cubic feet of lumber?
Answers
1) Considering that the amount of lumber in this Data Set has been normally distributed, then we can start by finding this Percentage (or probability in this interval, writing out the following expressions:
[tex]\begin{gathered} P(133Now we can replace it with the Z score formula, plugging into that the Mean, the Standard Deviation, and the given values:[tex]Z=\frac{X-\mu}{\sigma}[/tex]Then:
[tex]\begin{gathered} P(\frac{133-142}{9}<\frac{X-\mu}{\sigma}<\frac{169-142}{9}) \\ P(-1Checking a Z-score table we can state that the Percentage of the trees between 133 and 169 ft³ is:[tex]P(-12) Now, let's check for the second part, the number of trees. But before that, let's use the same process to get a percentage that fits into that:[tex]\begin{gathered} P(X>151)=\frac{151-142}{9}=1 \\ P(Z>1)=0.1587 \end{gathered}[/tex]Note that 0.1587 is the same as 15.87%. Multiplying that by the total number of trees we have:
[tex]18000\times0.1587=2856.6\approx2857[/tex]Rounding it off to the nearest whole.
3) Thus, The answers are:
i.84%
ii. 2857 trees
Function f is defined by f(x) = 2x – 7 and g is defined by g(x) = 5*
Answers
Answer
f(3) = -1, f(2) = -3, f(1) = -5, f(0) = -7, f(-1) = -9
g(3) = 125, g(2) = 25, g(1) = 5, g(0) = 1, g(-1) = 0.2
Step-by-step explanation:
Given the following functions
f(x) =2x - 7
g(x) = 5^x
find f(3), f(2), f(1), f(0), and f(-1)
for the first function
f(x) = 2x - 7
f(3) means substitute x = 3 into the function
f(3) = 2(3) - 7
f(3) = 6 - 7
f(3) =-1
f(2), let x = 2
f(2) = 2(2) - 7
f(2) = 4 - 7
f(2) =-3
f(1) = 2(1) - 7
f(1) = 2 - 7
f(1) =-5
f(0) = 2(0) - 7
f(0) =0 - 7
f(0) = -7
f(-1) = 2(-1) - 7
f(-1) = -2 - 7
f(-1) = -9
g(x) = 5^x
find g(3), g(2), g(1), g(0), and g(-1)
g(3), substitute x = 3
g(3) = 5^3
g(3) = 5 x 5 x 5
g(3) = 125
g(2) = 5^2
g(2) = 5 x 5
g(2) = 25
g(1) = 5^1
g(1) = 5
g(0) = 5^0
any number raised to the power of zero = 1
g(0) = 1
g(-1) = 5^-1
g(-1) = 1/5
g(-1) = 0.2
Reflected over the x-axis , horizontal shrink of 1/2, translated 7 down.
Answers
Given:
Reflected over the x-axis, horizontal shrink of 1/2, translated 7 down.
The parent function is y=|x|.
[tex]\begin{gathered} \text{reflected over x-axis=-f(x)} \\ \text{horizontal shrink=f(}\frac{x}{b}\text{)} \\ \text{translation to the down=f(x)-d} \end{gathered}[/tex]The function becomes,
[tex]y=-|2x|-7[/tex]Answer:
[tex]y=-|2x|-7[/tex]A cake is cut into 12 equal slices. After 3 days Jake has eaten 5 slices. What is his weekly rate of eating the cake?
5
36
35
36
cakes/week
cakes/week
1 cakes/week
35
01 cakes/week
Answers
The cake is divided into 12 equal slices. Jake had eaten 5 slices after 3 days. The weekly cake consumption rate is 11.6
What is algebraic expression?An algebraic expression is one that is composed of integer constants, variables, and algebraic operations. 3x2 2xy + c, for example, is an algebraic expression. Algebraic expressions have at least one variable and one operation (addition, subtraction, multiplication, division). 2(x + 8y) is an algebraic expression, for example. An algebraic expression is one that contains constants, variables, and algebraic operations. 3x2 2xy + d, for example, is an algebraic expression. Thus, an algebraic expression is composed of three types of fundamental elements: Coefficient (i.e. numbers) (i.e. numbers)Therefore,
The weekly cake consumption rate is 11.6
we have 7 days.
7days-3days =4
in 3 days he has eaten 5 slices
again 4-3 days=1
so in 6 days, he has eaten 10 slices
we have 1 day left.so if he eats 5 slices in 3 days, how many does he eat slices in 1 day?
5/3=1.6
10+1.6= 11.6
To learn more about algebraic expression, refer to:
https://brainly.com/question/4344214
#SPJ13
Isaiah is a plumber. One day he receives a house call from a potential customer in a differentcity. The distance on a map between his home and the customer's home is 8 inches. What isthe actual distance between Isaiah's home and the customer's home if the scale of the map is1 inch = 1 mile?
Answers
Given:
The distance on a map between his home and the customer's home, D=8 inches.
In the map, 1 inch=1 mile.
The actual distance between Isaiah's home and the customer's home is,
[tex]\begin{gathered} \text{Actual distance=8 inches}\times\frac{1\text{ mile}}{1\text{ inch}} \\ =8\text{ miles} \end{gathered}[/tex]Therefore, the actual distance between Isaiah's home and the customer's home is 8 miles.
Triangle FGH is similar to triangle IJK. Find the measure of side JK. Round youranswer to the nearest tenth if necessary.
Answers
Let x be the measure of JK so we get that
[tex]\frac{23}{5}=\frac{x}{3.5}\rightarrow x=3.5\cdot\frac{23}{5}=16.1[/tex]General Mills is testing 12 new cereals for possible production. They are testing 3 oat cereals, 5 wheat cereals, and 4 rice cereals. If each of the 12 cereals has the same chance of being produced,
and 4 new cereals will be produced, determine the probability that of the 4 new cereals that will be produced, 2 are oat cereals, 1 is a wheat cereal, and 1 is a rice cereal.
The probabilis
(Type an integer or a simplified fraction.)
Answers
Using the combination formula, the probability that of the 4 new cereals that will be produced, 2 are oat cereals, 1 is a wheat cereal, and 1 is a rice cereal is of 4/33.
Combination Formula[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
This formula is used when the order in which the objects are chosen is not important, as is the case in this problem.
A probability is given by the number of desired outcomes divided by the number of total outcomes.
For the total outcomes, 4 cereals are taken from a set of 12, hence:
[tex]T = C_{12,4} = \frac{12!}{4!8!} = 495[/tex]
For the desired outcomes, we have that:
2 oat are taken from a set of 3.1 wheat is taken from a set of 5.1 rice is taken from a set of 4.Hence the number is:
[tex]D = C_{3,2}C_{5,1}C_{4,1} = \frac{3!}{2!1!} \times \frac{5!}{1!4!} \times \frac{4!}{1!2!} = 3 \times 5 \times 4 = 60[/tex]
Hence the probability is:
p = 60/495.
Both numbers can be simplified by 5, hence:
p = 12/99.
They can also be simplified by 3, hence:
p = 4/33.
More can be learned about the combination formula at https://brainly.com/question/25821700
#SPJ1
What percent of 60 is 39?
Answers
Answer:
To find the percent of 60 is 39
Let x be the percent of 60 is 39,
we get,
[tex]\frac{x}{100}\times60=39[/tex]Solving this, we get
[tex]x=\frac{39\times10}{6}[/tex][tex]x=65[/tex]Hence 65 percent of 60 is 39.
Answer is: 65%
2) From an elevation of 38 feet below sea level, Devin climbed to an elevation of 92 feet abovesea level. How much higher was Devin at the end of his climb than at the beginning?
Answers
Ok, so he started at 38 feet below and ended at 92 feet above. 38 below = -38.
The difference in the height is given by
92-(-38) =
92+38 =
130 feet
Devin was 130 feet higher at the end of climbing.
For each level of confidence o below, determine the corresponding normal confidence interval. Assume each confidence interval is constructed for the same sample statistics.Drag each normal confidence interval given above to the level of confidence
Answers
Note that the width of the confidence interval increases as the confidence level increases.
Since the confidence intervals constructed are for the same sample statistic, the higher confidence interval will have a higher width.
The confidence levels have the following widths:
Therefore, the confidence intervals are matched such that the lowest interval has the smallest confidence level and the highest has the largest confidence level. This is shown below:
