Given:
The vector
[tex]v=<-3,8>[/tex]Required:
To find the unit vector u with the same direction.
Explanation:
Unit formula is the vector is divided by its magnitude.
Now the magnitude of v is,
[tex]\begin{gathered} mag.v=\sqrt{(-3)^2+8^2} \\ =\sqrt{9+64} \\ =\sqrt{73} \end{gathered}[/tex]Now the unit vector is,
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]Final Answer:
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]3. Find the value of the function h(x) = 2 when x = 10=
In order to find the value of h(x) when x=10, we replace the value of x along with the function by 10, however, since there are not any variables the function is constant for all variables
[tex]h(10)=2[/tex]A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible three topping pizzas (3 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with spicy italian sausage, banana peppers and beef. Express your answer as a fractionPizza toppings: Green peppers, onions, kalamata olives, sausage, mushrooms, black olives, pepperoni, spicy italian sausage, roma tomatoes, green olives, ham, grilled chicken, jalapeño peppers, banana peppers, beef, chicken fingers, red peppers
First, we need to find out how many possible combinations of pizza toppings there would be.
To do this, we will use the formula for Combination.
Combination is all the possible arrangements of things in which order does not matter. In our example, this would mean that a pizza topped with spicy Italian sausage, banana pepper, and beef is the same as a pizza topped with banana pepper, beef, and Italian sausage.
The formula for combination is
[tex]C(n,r)=^nC_r=_nC_r=\frac{n!}{r!(n-r)!}[/tex]From our given, n would be 17, since there are a total of 17 toppings (including spicy Italian sausage, banana peppers, and beef) and r would be 3 since there are three toppings that you chose.
Substituting it in the formula,
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex][tex]C(17,3)=\frac{17!}{3!(17-3)!}[/tex][tex]C(17,3)=680[/tex]Now, since we know that there are a total of 680 combinations of pizza toppings, we can now solve the probability of the first winner selecting a pizza topped with Italian sausage, banana peppers, and beef.
A resort rented 62 cabins during its first season in operation. Based on the data for a similar resort, management estimated the equation of the line of best fit for the number cabins rented as y= 4x + 62, where x is the number of seasons since the first season of operation, and y is the number of cabins rented during that season. In reality, unusually bad weather for several years beginning in the first season led to the number of rentals for each season decreasing at the rate they were expected to increase. Which is the best choice for the equation for the line of best fit for the cabin rentals?A) y = 1/4 + 62B) y = - 4x + 62C) y = - 1/4x + 62D) y = 4x - 62
In the equation y = 4x + 62, the increasing rate is 4
If the actual rate decreases at the rate they were expected to increase, then it is -4 instead of 4.
Then, the equation of the line is:
B) y = - 4x + 62
(a) Teresa owns 9 shares of a certain stock. Yesterday the total value of her shares went down by90 dollars. What was the change in value for each share?dollarsHelp ASAP PLEASE
we have that
Divide $90 by the number of shares
so
90/9=$10
the answer is $10
what would be an equation for a decrease of 75% using the y=kx format?
Input data
75% = 0.75
format
y = kx
Procedure
The k factor would be equal to 0.25
The answer would be
[tex]y=0.25x[/tex]We have seen the isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use information to the right to help the measure of angles 1, 2, 3, 4, and 5.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
triangle diagram
Step 02:
angles:
we must analyze the diagram to find the solution
angle 1:
angle 1 = 180° - 155° = 25°
angle 2:
angle 2 = angle 1 = 25°
angle 3:
angle 3 = 180° - 25° - 25° = 130°
angle 4:
angle 4 = 155°
angle 5:
angle 5 = 180° - 25° = 155°
That is the full solution.
What is the exact surface area of the right rectangular pyramid below? Leave your answer in simplified radical form.
Usually, to calculate the area of a solid we need to calculate the area of every face. Here we have a rectangle down, and four triangles. Our desired area (TA) will be the sum of those areas. Let's calculate those areas:
Area of the rectangle) The area of the rectangle (R) is
[tex]R=(leng\ldots)(wid\ldots)=(10cm)\cdot(4cm)=40\operatorname{cm}^2[/tex]Area of the front triangle and the back tringle) Note that the front triangle and the back triangle are the "same". So the area of each of them is equal (this simplifies our work...). The area of each of them (FB) is
[tex]FB=\frac{(base)\cdot(high)}{2}[/tex]What is their high?
The triangle with red, blue, and green edges is a right triangle... Its hypotenuse is the blue edge. We know the red edge, its length is 6cm, but what is the length of the green edge? Because our solid is a rectangular pyramid, we can say that the green edge is half of the length of the rectangle. that is, 5cm (10cm/2). Now, we know the red and green edges; so we can apply The Pythagoras theorem to get
[tex](blue)^2=(red)^2+(green)^2[/tex][tex](blue)^2=(6cm)^2+(5cm)2=36\operatorname{cm}+25\operatorname{cm}=61\operatorname{cm}^2[/tex][tex]undefined[/tex]How do you solve #16?
∠A + ∠B + ∠C = 180°
reason : Sum of all angle of triangle is 180°
72° + 86° + ∠C = 180°
158° + ∠C = 180°
∠C = 180° - 158°
∠C = 22°
hence the value of ∠3 is 22°
Now ,
∠3 =∠4
reason : Being vertically opposite angle
4 = 22°
hence the value of ∠4 is 22°
Again ,
∠C + ∠D + ∠E = 180°
reason : Sum of all angle of triangle is 180°
22° + ∠D + 70° = 180°
92° + ∠D = 180°
∠D = 180° - 92°
∠D = 88°
hence the value of ∠5 is 88°..
[tex]...[/tex]
hope it helps ....☘✨
Find an equation of the line. Write the equation using function notation.Through (4, - 7); perpendicular to 6y=x- 12The equation of the line is f(x)=..
To determine the equation of the line you need to determine its slope first.
You know that the line 6y=x-12 is perpendicular to the line you have to determine, two lines that are perpendicular, their slopes are opposite reciprocals. For example, let "m" represent the slope of one of the lines and "n" represent the slope of the perpendicular line, you can express their relationship as follows:
[tex]m=-\frac{1}{n}[/tex]To determine the slope of the given line, you have to write it in slope-intercept form:
[tex]y=mx+b[/tex]Where
m represents the slope
b represents the y-intercept
Given the line:
[tex]6y=x-12[/tex]-Divide both sides by 6
[tex]\begin{gathered} \frac{6y}{6}=-\frac{x}{6}=-\frac{12}{6} \\ y=-\frac{1}{6}x-2 \end{gathered}[/tex]The slope of this line is the coefficient of the x-term, n=-1/6
Its opposite reciprocal is:
[tex]\begin{gathered} m=-\frac{1}{n} \\ m=-(-\frac{1}{\frac{1}{6}}) \\ m=-(-1\cdot6) \\ m=-(-6) \\ m=6 \end{gathered}[/tex]The slope of the line you have to determine is m=6
Now that you have the slope of the line, using the point-slope form, you can determine the equation of the line:
[tex]y-y_1=m(x-x_1)[/tex]Where
m represents the slope of the line
(x₁,y₁) represent the coordinates of one point of the line
Replace the formula with m=6 and (x₁,y₁)=(4,-7)
[tex]\begin{gathered} y-(-7)=6(x-4) \\ y+7=6(x-4) \end{gathered}[/tex]The next step is to write the equation in slope-intercept form:
-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y+7=6\cdot x-6\cdot4 \\ y+7=6x-24 \end{gathered}[/tex]-Pass "+7" to the right side of the equation by applying the opposite operation "-7" to both sides of it:
[tex]\begin{gathered} y+7-7=6x-24-7 \\ y=6x-31 \end{gathered}[/tex]Finally, write the equation of the line using function notation:
[tex]f(x)=6x-31[/tex]Use the following data set to answer the question below.8 12 15 9 101212 18 14 1510 11 12 9 17What is the range for the data set?
Given the following set of data:
8 12 15 9 10 12 12 18 14 15 10 11 12 9 17
We will find the range of the data.
We need to find the maximum and the minimum
The maximum = 18
The minimum = 8
So, the range = maximum - minimum = 18 - 8 = 10
So, the answer will be The range = 10
help meeeeeeeeee pleaseee !!!!!
The value of the composite function is determined as: (g o f)(5) = 6.
How to Determine the Value of a Composite Function?To determine the value of a composite function, first evaluate the inner function by plugging in the value of x given, then use the output of the inner function as an input to evaluate the outer function.
Given the following:
f(x) = x² - 6x + 2
g(x) = -2x
Therefore:
(g o f)(5) = g(f(5))
Find f(5):
f(5) = (5)² - 6(5) + 2
f(5) = 25 - 30 + 2
f(5) = -3
Find g(f(5)) by substituting x = -3 into g(x) = -2x:
g(f(5)) = -2(-3)
g(f(5)) = 6
Therefore, (g o f)(5) = 6.
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Mrs. Maria's Market buys 75% of eggs from farm A and the rest from farm B. Of the eggs from A,8% are green, and of those from B, 3% are green. If an egg is chosen at random and found to begreen, what is the probability that the egg is from farm B? Enter your answer as a decimal numberrounded to TWO digits after the decimal point.
0.12
Explanations:What is probability?Probability is the likelihood or chance that an event will occur. It ca be expressed as:
[tex]Probability=\frac{n(E)}{n(S)}[/tex]where:
n(E) is the expected event
n(S) is the total sample space
If Mrs. Maria's Market buys 75% of eggs from farm A and the rest from farm B, the percentage amount of egg bought from B will be 25% (100-75)
n(S) = 25%
If 3% of the eggs from B are green, hence n(E) = 3%
Determine the required probability
Pr(egg is from farm B) = n(E)/n(S)
Pr(egg is from farm B) = 3/25 = 0.12
Hence the probability that the egg is from farm B is 0.12
Sue wants to plant 545 acres of wheat. She has planted a 128 acre field near the river. Whatpercent of her wheat crop has she planted?
Percentage of the wheat crop planted = 128/ 545 x 100
= 12800/545
= 23.4 percent
Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 3 years?
Answer:
The amount of interest she will be paid in the first 3 years is;
[tex]\text{ \$90}[/tex]Explanation:
Given that Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. for the first 3 years;
[tex]\begin{gathered} \text{ Principal P = \$500} \\ \text{rate r = 6\% = 0.06} \\ \text{time t = 3 years} \end{gathered}[/tex]Recall the simple interest formula;
[tex]i=P\times r\times t[/tex]substituting the given values;
[tex]\begin{gathered} i=500\times0.06\times3 \\ i=\text{ \$90} \end{gathered}[/tex]Therefore, the amount of interest she will be paid in the first 3 years is;
[tex]\text{ \$90}[/tex]See photo for problem
The distance, x, from one corner to another corner three corners away is 4. 70cm
The distance, y, from one corner to another corner two corners away is 4. 07cm
How to determine the valueIt is important to note that the image shown is a hexagon and each of the interior angles of a hexagon has a value of 120 degrees
Also note that the have the trigonometric identities;
sinecosinetangentcotangentsecantcosecantUsing the cosine identity, we have;
sin θ = adjacent/ hypotenuse
substitute the values
cos 60 = 2.35/x
cross multiply
x = 2. 35/cos 60
x = 2. 35/ 0. 5
x = 4. 7 cm
Then, we have,
sin 60 = y/ 4. 7
y = sin 60 × 4.7
y = 0. 8660 × 4. 7
y = 4. 07cm
Hence, the values are 4. 7cm and 4. 07cm
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In which quadrant is the terminal side of 115° located?+Y43-2+-XX+3 -111841.2IV3.4
ANSWER
Quadrant II
EXPLANATION
• All angles between 0° and 90° are in the first quadrant.
,• All angles between 90° and 180° are in the second quadrant.
,• All angles between 180° and 270° are in the third quadrant.
,• All angles between 270° and 360° are in the fourth quadrant.
115° is an angle measure that is between 90° and 180°. Therefore its terminal end is in the second quadrant.
Write the equation of this line in point-slope form: The line passes through (−2,22) and (4,-8).
Write the equation of this line in point-slope form: The line passes through (−2,22) and (4,-8).
step 1
Find the slope of the line
m=(-8-22)/(4+2)
m=-30/6
m=-5
step 2
Find the equation in point slope form
y-y1=m(x-x1)
substitute the given values
we have
m=-6
(x1,y1)=(4,-8)
substitute
y+8=-6(x-4)I will show you a pic
GIven the table above :
We have that
x y
2 8
4 4
6 0
8 4
The table represents a Non - Linear Function
Reason: It is because there is no constant ratio or proportion between x and y.
A red maple sapling was 3 feet tall when planted in 2010. Six years later, the tree was 24 feet tall. The growth rate of the tree is constant over time. Find a linear model for the height H (in ft) of the red maple t years after 2010. Let t = 0 represent 2010.H = __________What is the expected height (in ft) of the red maple in 2020?________ ft
Since the growth rate is linear and constant over time, it means that the sequence formed is an arithmetic sequence. The formula for finding the nth term of an arithmetic sequence is expressed as
an = a1 + d(n - 1)
where
a1 is the first term of the sequence
n = number of terms
d = common difference
In this case, n would be t(number of years
From the information given,
a1 = 3
Since the first term is at t = 0 and it represents 2010, six years letter would be represented by t = 7. Thus, we would took for d given that a7 = 24
We have
24 = 3 + d(7 - 1)
24 = 3 + 6d
6d = 24 - 3 = 21
d = 21/6 = 3.5
The linear model would be
an = 3 + 3.5(t - 1)
Substituting H for an, the linear model is
H = 3 + 3.5(t - 1)
At 2020, t = 11
H = 3 + 3.5(11 - 1) = 3 + 35
H = 38
There are 360° in a circle graph. If 50° of the graph represents rent and 7" of the graph represents savings, what fractional portion of the whole graph is not represented by rent and savings?
The fractional portion of the whole graph is not represented by rent and savings? is 101/120.
How to illustrate the information?From the information, there are 360° in a circle graph and 50° of the graph represents rent and 7" of the graph represents savings.
The part that isn't savings or rent will be:
= 360° - (7° + 50°)
= 360° - 57°
= 303°
Therefore, the fractional part will be:
= Part that isn't savings or rent / Entire degree
= 303/360
= 101 / 120
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A city has a population of 230,000 people. Suppose that each year the population grows by 4.25%. What will the population be after 12 years?
Answer:
379,001.
Explanation:
The population of the city grows by 4.25%.
This is a constant factor and models an exponential function.
An exponential population function is of the form:
[tex]\begin{gathered} P(n)=P_0(1+r)^t \\ P_o=\text{Initial Population} \\ r\text{ = growth rate} \\ t\text{ =time in years} \end{gathered}[/tex]From the given problem:
[tex]P_0=230,000,r=4.25\%=0.0425,t=12years[/tex]This then gives us:
[tex]\begin{gathered} P(12)=230000(1+0.0425)^{12} \\ =230000(1.0425)^{12} \\ =379,001 \end{gathered}[/tex]The population after 12 years will be approximately 379,001.
find the circumstances of the circle. use 3.14 for pi.
Given:
The radius of the circiel is 4.2 in.
The value of π is 3.14.
The objective is to find the circumference of the circle.
The formula to find the circumference of the circle is,
[tex]\begin{gathered} C=2\cdot\pi\cdot r \\ =2\cdot3.14\cdot4.2 \\ =26.376\text{ inches} \end{gathered}[/tex]Hence, the circumference of the circle is 26.376 inches.
PLEASE PLEASE HELP
5. Renae Walters is paid a salary of $15,000 per month.
a. How much has she earned for the year after being paid at the end of January? _______________________________
b. How much is deducted in January for Social Security? For Medicare?
Social Security _____________________ Medicare _______________________
c. How much has she earned for the year after being paid at the end of November? ___________________________________
d. How much is deducted in November for Social Security? For Medicare?
Social Security _____________________ Medicare _______________________
e. How much has she earned for the year after being paid at the end of December? ___________________________________
f. How much is deducted in December for Social Security? For Medicare?
Social Security _____________________ Medicare _______________________
The amount for social security for all 3 months will $930 and the contribution for Medicare will be $217.5.
How to estimate the amount for social security for all 3 month?Given that the salary exists paid in US dollars, we can consider that Renae Walters falls under the social security and Medicare tax rates for the United States. These rates, as of 2020, fall at 6.2% for social security and 1.45% for Medicare.
Social security contribution = Social security tax rate × Income earned
January for example Social Security = 0.062 × $15,000 = $930
Medicare contribution = Medicare tax rate × Income earned
January for example Medicare = 0.0145 × $15,000= $217.5
The above method will apply through the months without changes.
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An angle bisector is a ray that divides an angle into two angles with equal measures. If OX bisects ZAOB and mZAOB 142, what is the measure of each of the
angles formed? (Note: Round your answer to one decimal place).
Measure of each of the angles formed between ZAOB is 71° using angle bisector theorem.
What is the angle bisector?In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.
m(ZAOB)=142°
OX will bisect ZAOB in equal angel both side.
So m(ZAOX) is 71°
And also, m(ZAOB) is 71°
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8y = 0.2(3x - 5) answer in slope intercept and y-intercept
The slope of the given equation is 0.075 and y-intercept is 0.125
What is slope of line ?
Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.
The point with coordinate having same slope as with given coordinates can be plotted on the same line.
First writing the given equation in standard slope intercept form :
y = mx + c.........(1)
In which:
• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
• c is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function
8y = 0.2(3x - 5)
8y = 0.6x - 1
y = 0.6/8x - 1/8
y = 0.075x - 0.125
Now, comparing it with equation (1) we get :
m = 0.075 and c = - 0.125
hence the slope of the given equation is 0.075 and y-intercept is 0.125
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the cake is regular price at $9 and is on sale for 25%. how much would you save with the discount
Let be "x" the amount of money (in dollars) you would save with the discount.
By definition, a percent can be converted to a Decimal number by dividing it by 100. Then, since the cake store is having 25% off sale on all cakes, this can be written as:
[tex]\frac{25}{100}=0.25[/tex]According to the information given in the exercise, the regular price of the cake you want is $9. Based on this, you can set up the following expression for price of the cake with the discount (in dollars):
[tex]9-(9)(0.25)[/tex]Evaluating, you get:
[tex]=6.75[/tex]Knowing this value, you can set up that:
[tex]x=9-6.75[/tex]Finally, evaluating, you get:
[tex]x=2.25[/tex]The answer is: You would save $2.25 with the discount.
Fill in the missing statements and reasons in each proof shown below. You must mark the diagram forcredit.15.Given: g | h and 21 22Prove: p | r3рStatementReason2.ghgh21 2 2321 2222 223pllr
To prove that p || r, we will complete the data in the given table
[tex]\begin{gathered} \text{Statement: g}\mleft\Vert h\mright? \\ R\text{eason : Given} \end{gathered}[/tex][tex]\begin{gathered} \text{Statement: <1}\cong<3 \\ \operatorname{Re}\text{ason: Corresponding angles} \end{gathered}[/tex][tex]\begin{gathered} \text{Statement: <1}\cong<2 \\ \operatorname{Re}\text{ason:Given} \end{gathered}[/tex][tex]\begin{gathered} Statement\colon\text{ <2}\cong<3 \\ Re\text{ason: Alternate exterior angle} \end{gathered}[/tex][tex]\begin{gathered} \text{Statement: P}\mleft\Vert r\mright? \\ \operatorname{Re}\text{ason:<2}\cong<3 \end{gathered}[/tex]Find the missing number so that the equation has no solutions.
5x + 12 =
- 2
Submit
By solving the equation 5x + 12 = -2, the value of x in is -2.8
Solution
Bring 12 to the other side of the equation. 12 becomes -125x = -2-12
Add -2 and -12.5x = -14
We get -14
Bring 5 to the other side of the equation and divide -14 and 5x = -14 ÷ 5
Hence the value of x is -2.8x = -2.8
Hence, by solving the equation 5x + 12 = -2, the value of x in is -2.8
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what is the equation of the line with x-intercept (6,0) and y-intercept (0, 2)
Answer:
3y=6-x
Explanation:
The slope-intercept form of a line is y=mx+b.
First, we determine the slope(m) of the line.
[tex]\begin{gathered} m=\frac{2-0}{0-6} \\ =-\frac{2}{6} \\ m=-\frac{1}{3} \end{gathered}[/tex]Since the y-intercept, b=2
The equation of the line is:
[tex]\begin{gathered} y=-\frac{1}{3}x+2 \\ y=\frac{-x+6}{3} \\ 3y=6-x \end{gathered}[/tex]Complete the description of the piece wise function graphed below
Analyze the different intervals at which the function takes the values provided by the graph. Pay special attention on the circles, whether they are filled up or not.
From the graph, notice that the function takes the value of 3 when x is equal to -4, -2 or any number between them. Therefore, the condition is:
[tex]f(x)=3\text{ if }-4\leq x\leq-2[/tex]If x is greater (but not equal) than -2 and lower or equal to 3, the function takes the value of 5. Therefore:
[tex]f(x)=5\text{ if }-2Notice that the first symbol used is "<" and the second is "≤ ".Finally, the function takes the value of -3 whenever x is greater (but not equal) to 3 and less than or equal to 5. Then:
[tex]f(x)=-3\text{ if }3In conclusion:[tex]f(x)=\mleft\{\begin{aligned}3\text{ if }-4\leq x\leq-2 \\ 5\text{ if }-2