about 23% of people are at a higher risk of stroke due to other medical conditions like high blood pressure. their risk is about 9% of stroke compared with the general population's 3% chance of having a stroke in their lifetime.
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Write a linear function f with f(0) = 3.75 and f(-6) =3.75
f(x) = ???
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The linear function will be;
⇒ f (x) = 3.75
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values are,
⇒ f (0) = 3.75
And, f (-6) = 3.75
Now,
Let the linear function is,
f (x) = ax + b
Since, The values is given as;
f (0) = 3.75
And, f (-6) = 3.75
So, We can substitute the given values in the linear function, we get;
f (x) = ax + b
Substitute x = 0 we get;
f (0) = a × 0 + b
f (0) = b
3.75 = b
b = 3.75
And, We can substitute x = -6 and f(0) = 3.75 we get;
f (-6) = a × -6 + b
3.75 = -6a + 3.75
- 6a = 0
a = 0
So, Substitute a = 0 and b = 3.75 in linear function we get;
f (x) = ax + b
f (x) = a × 0 + 3.75
f (x) = 3.75
Therefore,
The linear function will be;
⇒ f (x) = 3.75
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What’s eight less than four times a number in algebraic expression
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Answer:
4x - 8, 4x just means four of x, and eight less means to subtract 8.
Step-by-step explanation:
Answer:
The answer is 4x - 8 and it equals -32
I need help with solving residential plots and correlation vs causation how do I solve a liner model from the data ?
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The image shows point that have a value that is close to zero, so they are small values
In the question, they say that those points represent the residual plot, that means that they represent the error of the linear model
The error is very small, close to zero
So the residual plot shows a non-random pattern, becuase all the point are close to zero
And then the date can be represented by a linear model
So the answer for the left box is "non-random"
And for the right box is "linear"
On the left box:..... non-random
On the right box...... linear
Question 8 of 20If f(x) = 2x²+2 and g(x)=x2-1, find (f- g)(x).O A.3x²+3O B.x2²+1 O C.3x2² +1O D.x² +3
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Solution
Step 1
Write the two functions:
[tex]f\mleft(x\mright)=2x²+2\text{ }and\text{ }g\left(x\right)=x2-1[/tex]Step 2
(f- g)(x) = f(g) - g(x)
[tex]\begin{gathered} \left(f-g\right)\left(x\right)=2x²+2\text{ - \lparen}x^2-1) \\ \\ (f-g)(x)=2x^2+\text{ 2 - x}^2\text{ + 1} \\ \\ (f-g)(x)=x^2+3 \end{gathered}[/tex]Final answer
D. x² +3
do you know the north Zone at the football stadium has 95 Rose there are 48 seats in a row how many people will the North end zone seat
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The North zone at the football stadium has 95 rows.
There are 48 seats in a row.
How many people will the North end zone seat?
Since there are 95 rows and each row has 48 seats, multiply them to get the total number of seats.
[tex]\begin{gathered} total\: seats=rows\times seats \\ total\: seats=95\times48 \\ total\: seats=4560 \end{gathered}[/tex]Therefore, there are 4560 people sitting in the North zone.
in this quadratic trinomial 20 is the _____. 3x^2 -7x-20
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A trinomial has three terms. The first term contains the squared variable, the second term contains the variable with an exponent of 1, and the third term does not have any variable. That term is called the independent term.
In the polynomial:
[tex]3x^2-7x-20[/tex]The term -20 is the independent term because it does not depend on the value of the variable x.
What is the coefficient of the second term in this expression?-k + 10m² - 6 - n² ?
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Given the expression:
[tex]-k+10m^2-6-n^{2^{}}[/tex]The second term in the expression means the 2nd term from left to right of an expression.
Here, the second term is 10m².
A coefficient is a number that is being multiplied by the variable.
Therefore, the coefficient of the term 10m² is 10.
The diameter of a circle is 6 ft. Find its circumference in terms of \piπ.
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The circumference of circle with diameter 6 feet will be 6π feet.
According to the question,
We have the following information:
Diameter of the circle = 6 feet
Now, we will find the radius of the circle. We know that the radius of the circle is half that of its diameter.
Radius of the circle = Diameter/2
Radius of the circle = 6/2 feet
Radius of the circle = 3 feet
We know that the following formula is used to find the circumference of the circle:
Circumference of the circle = 2πr
Circumference of the circle = 2π*3
Circumference of the circle = 6π feet
Hence, the circumference of the circle is 6π feet.
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A pair of jeans is on sale for $30. If this price represents a 20% discount from the original price, what is the original price to the nearest cent ?
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Given Data:
The sale price of the jeans is: s=$30
The discount is: d=20%
The expression to calculate the original price is,
[tex]s=P\times\frac{d}{100}[/tex]Here P represents the original price.
[tex]\begin{gathered} 30=P\times\frac{20}{100} \\ P=30\times\frac{100}{20} \\ =30\times5 \\ P=150 \end{gathered}[/tex]Thus, the original price of the jeans is $150.
Find the volume of a cylinder and cinema given the following dimensions
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Given:
The radius , r=20 ft.
The height , h=23 ft.
The volume of the cylinder can be calculated as,
[tex]\begin{gathered} V=\pi r^2h \\ =\pi\times20^2\times23 \\ =28902.65ft^2 \end{gathered}[/tex]Therefore, the volume of the cylinder is 28902.65 sq.ft.
The volume of the cone can be calculated as,
[tex]\begin{gathered} V=\frac{1}{3}\pi\times r^2h \\ =\frac{1}{3}\pi\times20^2\times23 \\ =9634.22ft^2 \end{gathered}[/tex]Therefore, the volume of the cone is 9634.22 sq.ft.
A company purchased 10,000 pairs of men'sslacks for $18.66 per pair and marked them up $22.93. What was the selling price of each pair of slacks? Use the formulaS=CMThe selling price of each pairs of slacks is ?
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Given:
A company purchased slacks for $18.66 per pair.
Mark up= $22.93
[tex]\begin{gathered} \text{Selling price= cost price +mark up} \\ \text{Selling price=}18.66+22.93 \\ \text{Selling price= \$41.59} \end{gathered}[/tex]What is the value of f(-5) in the piecewise function -3x + 1 when x > 1 f(x) = -2x when x = 1 2x - 1 when x < 1
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Answer:
f(-5)=-11
Explanation:
Given the piecewise function:
[tex]f(x)=\begin{cases}{-3x+1,\text{ when }x>1} \\ {-2x,\text{ when }x=1} \\ {2x-1,\text{ when }x<1}\end{cases}[/tex]We want to find the value of f(-5).
When x=-5:
[tex]\begin{gathered} -5<1\implies f(x)=2x-1 \\ \text{ Therefore:} \\ f(-5)=2(-5)-1 \\ =-10-1 \\ =-11 \end{gathered}[/tex]The value of f(-5) is -11.
q divided by 4 + 8q, for q=8
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We have to calculate the value of the expression:
[tex]\frac{q}{4+8q}[/tex]when q = 8.
To calculate this, we replace q with its value and solve as:
[tex]\frac{q}{4+8q}=\frac{8}{4+8\cdot8}=\frac{8}{4+64}=\frac{8}{68}=\frac{2}{17}[/tex]Answer: 2/17
Can you help me with this problem? I will send a screenshot of the problem and the answer choices.
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Given:
Distance of her beagle = 25/4 meters to the right
Distance of her labrador = 51/20 meters directly to her left.
Let's determine the expression which represents how far apart the two dogs are.
We have the following:
Since the beagle is to the right, the distance is = 25/4 meters
Since the labrador is to the left, the distance is = -51/20 meters.
Now, to find how far apart the two dogs are, let's use the absolute value expression:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})|[/tex]Therefore, the expression which represents how far the two dogs are is:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})\rvert[/tex]ANSWER:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})\rvert[/tex]Determine the effect on the graph of the parent f(x)=x
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To answer this question we first graph the parent function
Now we compare the two graphs. We notice that the graph shown is translated two units up.
To translate the graph of function we have to add the ammount we want to translate, then in this case
[tex]g(x)=f(x)+2[/tex]Therefore the answer is J.
1. 3 In right AXYZ, the length of the hypotenuse YZ is 85 inches and tan Z= 3/4 What is the length, in inches, of the leg XY?
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We have a right triangle XYZ.
The length of the hypotenuse is YZ=85.
We also know that the tangent of Z is 4.
We have to find the length of XY.
We can start by drawing the triangle and writing the data:
The tangent of an angle can be related with the sides by the following trigonometric ratio:
[tex]\tan (Z)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{XY}{XZ}=\frac{3}{4}[/tex]We can not find the value of the legs from the trigonometric ratio, but we have a proportion between them. We can write the previous result as:
[tex]\begin{gathered} \frac{XY}{XZ}=\frac{3}{4} \\ XZ=\frac{4}{3}\cdot XY \end{gathered}[/tex]Now we can relate XY with the hypotenuse YZ using the Pythagorean theorem:
[tex]\begin{gathered} XY^2+XZ^2=YZ^2 \\ XY^2+(\frac{4}{3}XY)^2=YZ^2 \\ XY^2+\frac{16}{9}XY^2=YZ^2 \\ (\frac{16}{9}+1)XY^2=YZ^2 \\ \frac{16+9}{9}XY^2=YZ^2 \\ \frac{25}{9}XY^2=YZ^2 \\ XY^2=\frac{9}{25}YZ^2 \\ XY=\sqrt[]{\frac{9}{25}YZ^2} \\ XY=\frac{3}{5}YZ \\ XY=\frac{3}{5}\cdot85 \\ XY=51 \end{gathered}[/tex]Answer: the length of the leg XY is 51 inches.
Which system of equations best represents the situation below?A farmer grew his own tomatoes (a), eggplants (b), and potatoes (c). Hedecided to package his vegetables and price them as follows:1 tomato, 1 eggplant, 2 potatoes for $102 tomatoes, 1 eggplant, 3 potatoes for $144 tomatoes, 3 eggplants, 5 potatoes for $20
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Solution
- The cost of the crops are $(a) for tomatoes, $(b) for eggplants, and $(c) for potatoes.
- We simply need to follow the statements about the farmer's pricing in order to determine the correct set of equations.
Statement 1:
- "1 tomato, 1 eggplant, 2 potatoes for $10"
- If there is 1 tomato, it implies that, this tomato is priced at $(a). Similarly, 1 eggplant would be priced at $(b), but 2 potatoes would be $(c) + $(c) = $2(c).
- We are told that the total cost for this package is $10.
- Thus, the first equation must be:
[tex]a+b+2c=10[/tex]- We can interprete the other packages in a similar manner.
Statement 2:
"2 tomatoes, 1 eggplant, 3 potatoes for $14"
- This implies that the farmer would price the packages as follows:
2 tomatoes: 2(a)
1 eggplant: 1(b)
3 potatoes: 3(c)
- Since the total cost is $14, we can write the second equation as follows:
[tex]2a+b+3c=14[/tex]Statement 3:
"4 tomatoes, 3 eggplants, 5 potatoes for $20"
- This implies that the farmer would price the packages as follows:
4 tomatoes: 4(a)
3 eggplants: 3(b)
5 potatoes: 5(c)
- Since the total cost is $20, we can write the third equation as follows:
[tex]4a+3b+5c=20[/tex]Final Answer
The 3 equations are:
[tex]\begin{gathered} a+b+2c=10 \\ 2a+b+3c=14 \\ 4a+3b+5c=20 \end{gathered}[/tex]OPTION C
1: Are the two slopes parallel.
perpendicular or neither?
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The slopes of two parallel lines are the same, while the slopes of two perpendicular lines are the opposite reciprocals of each other. Each line has infinitely many lines that are parallel to it and infinitely many lines that are perpendicular to it.
P.S hopes this helps
Help please not sure if I am right or wrong thank you
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Given:
[tex]-1+\sqrt[]{-4}[/tex]To find the simplified complex number
[tex]\begin{gathered} -1+\sqrt[]{-4}=-1\pm2i \\ -1+\sqrt[]{-4}=-1+2i,-1-2i \end{gathered}[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
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Answer:
it would be the same since reflection doesn't change the andle
Answer:
A: It would have the same measure as the original angle.
Step-by-step explanation:
Well, reflecting is where you take the original image, which you see now, and flipping it like a mirror image. So, I think the answer would be: A It would have the same measure as the original angle. Because, it is literally the same thing, just in a mirror image. Like, if you look in the mirror, you see yourself, still the same.
x- sq root 6 is a factor of x^4-36 true or false
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We want to know if (x-sqroot(6)) is a factor of (x^4 - 36)
That's mean:
[tex](x^4-36)=(x-\sqrt[]{6})\text{ P(x)}[/tex]Where P(X) is a polinomial.
In this case, if x = sqroot(6) the polinomail (x^4 - 36) must be zero, that's mean sqroot(6) is a root (or a zero) of (x^4-36).
So, if we evaluate (x^4 - 36) in x=sqroot(6):
[tex](\sqrt[]{6})^4-36=6^2-36=0[/tex]So, the answer is true.
How many area codes of the form (XYZ) are possible if the digit 'X' and 'Y' can be any number ( through 9 but they can't repeat and the digit 7 can be any number 1 through 9?
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Start to see the possible options
[tex]XYZ=-\cdot-\cdot-_{}[/tex]The first digit will have 10 possible numbers to choose from 0 to 9, however in the second digit since it cannot repeat there will be only 9 possible to choose from. As for ther third number 0 is not an option meaning that there are 9 to choose as well.
[tex]\begin{gathered} XYZ=10\cdot9\cdot9 \\ XYZ=810 \end{gathered}[/tex]Given the figure below, determine the angle that is a same side interior angle with respect to
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We remember that two interior angles are those inside the are of the lines, Thus, the angles in the area:
Are interior. Now, we identify two sides, the right side, and the left side, which have been separated by the transversal line.
Thus, the angle that is is the same side as ∡3, and also that is interior is ∡5.
Error Analysis On a math test a student, Sarah, has to identify all the coefficients and constantsof the expression y +n + 2. Sarah says that 6 is a coefficient and 2 is a constant. Identify all thecoefficients and constants of the expression. What error might Sarah have made?The coefficient(s) of the expression is/are
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the coefficients are the numbers that accompany a variable on this case we have 2 variables y and n so the numbers that accompany each one are 1 for y and 6 for n
so there area 2 coefficients 1 and 6
the constant are the numbers without a variable on this case only the 2
27–34: Describing Distributions. Consider the following distributions.-How many peaks would you expect the distribution to have? Explain.-Make a sketch of the distribution.-Would you expect the distribution to be symmetric, left-skewed, or right-skewed? Explain.-Would you expect the variation of the distribution to be small, moderate, or large? Explain.#29The annual snowfall amounts in 50 randomly selected American cities
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Answer:
Step-by-step explanation:
Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB=10 feet, and BE and BD trident angle ABC, what is the perimeter of the deck area to the right of the beam of light ?PART 1: what others angles or sides of triangle BDC can you label given that side AB is 10 feet, BE and BD trisect angle ABC? Label the diagram accordingly, and explain your reasoning
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Part 1
The labelled disgram is shown below.
We would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
Considering triangle ABE
Sin 60 = 10/BE
BE = 10/Sin60 = 11.55
tan60 =10/AE
AE = 10/tan60 = 5.77
Part 1
Side DC of triangle BDC = 10 feet(opposite sides of a rectangle are congruent)
angle DBC = 30 degrees because BE and BD trisect angle ABC. 90/3 = 30
The sum of the angles in a triangle is 180 degrees. Thus,
angle DBC + angle DCB + angle BDC = 180
30 + 90 + angle BDC = 180
angle BDC = 180 = 180 - (30 + 90 = 180 - 120
angle BDC = 60
Sin 30 = CD/BD = 10/BD
BD = 10/Sin30
BD = 20
tan 30 = DC/BC = 10/BC
BC = 10/tan30
BC = 17.32
Perimeter of deck area to the right of the beam of light = perimeter of triangle BDC
= BD + DC + BC
= 20 + 10 + 17.32
Perimeter = 47.32 feet
Evaluate each function. Be sure to show your substitutions.h(x) = 7x^2 - 4x-15h(20)
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The function is given as,
[tex]h(x)=7x^2-4x-15[/tex]The objective is to determine the value h(20).
This can be obtained by substituting 20 for 'x' in the given expression,
[tex]\begin{gathered} h(20)=7(20)^2-4(20)-15 \\ h(20)=7(400)-80-15 \\ h(20)=2800-95 \\ h(20)=2705 \end{gathered}[/tex]Thus, the value of the given function h(20) is 2705.
Jason enjoys watching the squirrels in his neighborhood park. They eat the red oak acorns. After the city removed 4 diseased red oak trees, the population of squirrels decreased from 105 to 98 in one year. If the population continues to decline at the same rate, how many squirrels will live in the park in 15 years? First, calculate the rate of decay by subtracting the two populations and dividing the difference by the initial population. Then, use the formula A=a0e^kt
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given parameters
[tex]\begin{gathered} Initial\text{ squirrels}=105 \\ Num\text{ber of squirrels after one year}=98 \\ change\text{ in number of squirrels in a year}=105-98=7 \\ chan\text{ge in diseased oak trees}=y-4 \end{gathered}[/tex]STEP 2: Calculate the rate of decay (k)
[tex]\begin{gathered} rate\text{ of decay\lparen k\rparen}=\frac{Final\text{ population-Initial population}}{initial\text{ population}} \\ \text{By substitution,} \\ k=\frac{98-105}{105}=\frac{-7}{105}=-0.06666666\approx-0.0667 \end{gathered}[/tex]STEP 3: Calculate the number of squirrels after 15 years
[tex]\begin{gathered} A=a_0e^{kt} \\ a_0=105 \\ k=-0.0667 \\ t=15 \end{gathered}[/tex]By substitution,
[tex]A=105\cdot e^{-0.0667\times15}[/tex]By simplification,
[tex]\begin{gathered} \mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b} \\ =105\times \frac{1}{e^{15\times \:0.0667}} \\ \mathrm{Multiply\:fractions}:\quad \:a\times \frac{b}{c}=\frac{a\:\times \:b}{c} \\ =\frac{1\times \:105}{e^{1.0005}} \\ \mathrm{Multiply\:the\:numbers:}\:1\times \:105=105 \\ =\frac{105}{e^{1.0005}} \\ e^{1.0005}=2.71964 \\ =\frac{105}{2.71964} \\ \mathrm{Divide\:the\:numbers:}\:\frac{105}{2.71964}=38.60803 \\ =38.60803 \end{gathered}[/tex]By approximation, this leaves us with 34 squirrels
Ashley watches a giant that has 16 equally spread seats. Identify w.
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The angle formed outside the circle by the intersection of a tangent and a secant is equal to half of the difference of the intercepted arcs. The bigger arc is 180º, because the starting point of the secant and the starting point of the tangent are precisely on the opposite position of each other(we can see that by counting the same amount of seats between them on both sides). The smaller arc is equal to 90º, therefore
[tex]w^o=\frac{1}{2}(180^o-90^o)=45^o[/tex]Write in terms of confunction of a complementary angle:tan 26°
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ANSWER
The cofunction of tan 36 degrees is cot 54 degrees
STEP-BY-STEP EXPLANATION
Given information
[tex]\text{tan 26}\degree[/tex]Co function of tan can be written below as
[tex]\begin{gathered} \tan \text{ }(A)\text{ = cot (B)} \\ \text{if, A + B = 90} \end{gathered}[/tex][tex]\begin{gathered} \text{tan 36 = cot (90 - 36)} \\ \tan \text{ 36 = cot 54} \end{gathered}[/tex]Therefore,
tan 36 = 0.7265
cot 54 = 0.7265
Hence, the cofunction of tan 36 is cot 54