The actual distance is 90 miles between the town and the state capital based on the scale of the map
1/2 inch on the map = 10 miles
So, 1 inch = 20 miles
Distance between the town and state capital = 4 1/2 inches
The mathematical relationship between a small unit of measurement on a map, such as an inch or centimetre, and the corresponding real-world unit of distance, such as a kilometre or a mile, is known as a map scale.
The actual distance in miles between the town and the state capital is given by:
Distance between town and state capital* Scale of the map
= 4.5*20
= 90 miles
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Out of 250 tickets in a raffle, one ticket will win a $980 prize, one ticket will win a $680 prize, and one ticket will win a $470 prize. The other tickets will win nothing. If you have a ticket, what is the expected payoff?
The expected value is given as:
[tex]E(x)=\sum ^{}_{}xP(x)[/tex]then in this case we have:
[tex]\begin{gathered} E(x)=980(\frac{1}{250})+680(\frac{1}{250})+470(\frac{1}{250}) \\ =8.52 \end{gathered}[/tex]therefore the expected payoff is $8.52
Which of the following hypotheses is not a valid null hypothesis?a.H0: µ = 0b.H0: µ ≥ 0c.H0: µ ≤ 0d.H0: µ < 0
Given:
a. H0: µ = 0
b. H0: µ ≥ 0
c. H0: µ ≤ 0
d. H0: µ
Required:
To choose the hypotheses that is not valid.
Explanation:
The null hypothesis: It is a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
Here the option d is not valid.
Final Answer:
The option d is not valid.
H0: µ < 0
jermey wants to buy a new computer the sales woman says that he can make a down payment and then pay for the computer in installments here is the formula for this scex=t-yzx= amount down y=money each month z=number of months t= total price rewrite the formula to solve for the total price of the computer
ANSWER:
[tex]t=x+yz[/tex]STEP-BY-STEP EXPLANATION:
We have the following formula for the statement
[tex]x=t-yz[/tex]They ask us to rewrite this formula solving for the total price of the computer, it would be like this:
[tex]\begin{gathered} t-yz=x \\ t-yz+yz=x+yz \\ t=x+yz \end{gathered}[/tex]111 pointFind cot(1.570/7.3). Round to 3 decimal places.Type your answer...
If translation T maps point A(-3, 1) onto point A'(5, 5),
which is the translation T?
Answer: [tex](x,y) \to (x+8, y+4)[/tex]
==================================================
Explanation:
The x coordinate of A and A' are -3 and 5 respectively.
This is an increase of +8 since -3+8 = 5
Therefore, we shift the preimage 8 units to the right to get the image point.
That explains how x turns into x+8.
-------------
The y coordinates of A and A' are 1 and 5 respectively.
This is an increase of +4, so we shift the preimage up 4 units.
This signals that y turns into y+4
--------------
To recap we found that,
x becomes x+8y becomes y+4Therefore we get to the answer [tex](x,y) \to (x+8, y+4)[/tex]
--------------
To check the answer, let's apply this translation to point A(-3,1) and we should get (5,5) as the result.
[tex](\text{x},\text{y})\to(\text{x}+8,\text{y}+4)\\\\(-3,1)\to(-3+8,1+4)\\\\(-3,1)\to(5,5)\\\\[/tex]
This confirms the answer is correct.
plsssssss i need hdelpppppp plss 20 points on the line
Answer:d is the correct answer.
Step-by-step explanation:
Point B is located at (-5, -5) on the coordinate plane. Point B is reflected over thex-axis to create point B'. What ordered pair describes the location of B'?
SOLUTION
If a coordinate is refleted over the x-axis, the formula to apply is
[tex](x,y)\rightarrow(x,-y)[/tex]So for B(-5, -5), this becomes
[tex]\begin{gathered} B\mleft(-5,-5\mright)\rightarrow(-5,-(-5) \\ \\ the\text{ answer becomes } \\ \\ B(-5,-5)\rightarrow B^{\prime}(-5,5) \end{gathered}[/tex]Is -36/6 a integer number
Answer:
Yes
Step-by-step explanation:
-36/6 = -6
Integers are the whole numbers (0.1.2.3.4.5....) and their opposites ...-4,-3,-2,-1
Find the solution.7 · x = 8412139177
We need to find the value for x using the inverse operation:
Then:
[tex]\begin{gathered} 7-x=84 \\ \end{gathered}[/tex]Let us solve for x:
The x is subtracting, so it will add up to the other side:
[tex]7=84+x[/tex]Now, the 84 is positive, so it will be negative on the other side:
[tex]\begin{gathered} 7-84=x \\ x=-77 \end{gathered}[/tex]Hence, the solution for x is -77.
Given that f ( x ) = 3 x − 6 f ( x ) = 3 x - 6 and g ( x ) = 2 − x 2 g ( x ) = 2 - x 2 , calculate
If it is given f(x) = 3x− 6 and g(x) = 2- x² then f(g(x)) = -6x².
To solve this problem we have to know more about mathematical functions.
What is a mathematical function?
A mathematical function is a such type of mathematical device as it establishes a special type of relation which provides an output concerning an input.
Example: f(x) = x²+ 2 where f(x) is a function of x where x is the input. If x = 3 then the output value of f(x) = 3²- 2 = 9-2 = 7.
Here we have to calculate, f(g(x)) where f is a function of g(x) and g(x) is a function of x.
g(x) = 2- x².
f(x) = 3x - 6.
Therefore,
f(g(x)) = 3( 2- x² ) - 6. [where g(x) = 2- x²]
So, f(g(x)) = 3( 2- x² ) - 6 = 6 -6x² -6 = -6x²
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The complete question:
Given that f(x) = 3x − 6 and g(x) = 2 - x² , calculate f(g(x))
p and q are both prime numbers. They are each less than 22 Give an example where p + q is odd but not prime. You must only write the two numbers in the answer box. Type here to search O RI e Total ma
Answer:
See below
Step-by-step explanation:
2 + 7 = 9 2 and 7 are prime the answer is odd but not prime
please help me out fr
Christian, this is the solution to the problem:
p = 2l + 2w
Solving for l, we have:
2l = p - 2w
Dividng by 2 at both sides:
2l/2 = (p - 2w)/2
l = (p - 2w)/2
The correct answer is D.
#3 TV Aspect RatioUsing your knowledge of aspect ratios, find the difference between the actualscreen size or area of an older style TV with an aspect ratio of 4:3 and a newer TVwith an aspect ratio of 16:9. Assume that both TV's are 52 inches in height. Whatis the difference in the areas of the two TV's? (show all work and justify youranswer) (8 points)
3:4 ratio
height: 52 in
width: height * 4/3 = 52*4/3 = 208/3 in
Area of the TV: height*width = 52*208/3 = 3605 1/3 square inches
9:16 ratio
height: 52 in
width: height * 16/9 = 52*16/9 = 832/9 in
Area of the TV: height*width = 52*832/9 = 4807 1/9 square inches
Then, the difference in the areas is: 4807 1/9 - 3605 1/3 = 1201 7/9 square inches
An air traffic controller spots two planes flying at the same altitude. Their flight paths form a right angle at point P. One plane is 150 miles from point P and is moving at 440 miles per hour. The other plane is 200 miles from point P and is moving at 440 miles per hour. Write the distance s between the planes as a function of time t.
The distance s as a function of time is s = 50√(162t² -126t +25)
Take miles and hours to be the problem's units.
The distance of the first plane from point p is provided by
x = 150 -450t
The distance of the second plane from point p is given by
y = 200 -450t
The Pythagorean theorem can be used to calculate the distance between them because their flight trajectories are at right angles (s).
s² = x² + y²
s² = (150 -450t) (150 -450t)
² + (200 -450t)² = 22500 -135000t +202500t² +40000 -180000t +202500t²
... s² = 40500t² -315000t +62500 = 2500(162t² -126t +25)
... s = 50√(162t² -126t +25)
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Here’s the question to solve. Just do the question that has the chart
Step 1:
Write the equation
[tex]x^4-x^3+3x^2\text{ - 9x }-\text{ 54 = 0}[/tex]Step 2:
Use trial and error to find one the the factor
x - 3 is a factor
Because when you substitute x = 3, the result is zero
Hence, 3 is zero of the polynomial
Step 3
Use the long division
how do I put 5/7-i in standard form?
To put
[tex]\frac{5}{7-i}[/tex]In the standard form, we must multiply the numerator and denominator by the complex conjugate of (7-i), it means
[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}[/tex]And now we solve it, therefore
[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}=\frac{5(7+i)}{7^2-i^2}[/tex]Remember that
[tex]i^2=-1[/tex]Then
[tex]\begin{gathered} \frac{5(7+i)}{7^2-i^2}=\frac{5(7+i)}{49+1} \\ \\ \frac{5(7+i)}{49+1}=\frac{5(7+i)}{50} \end{gathered}[/tex]Now we can simplify it
[tex]\frac{5(7+i)}{50}=\frac{7+i}{10}[/tex]And we have it in the standard form
[tex]\frac{7}{10}+\frac{1}{10}i[/tex]. Which units can be used to measure distance?
A. seconds
B. cubic centimeters
C. meters
D. liters
Answer:
c
Step-by-step explanation:
The metre or meter, symbol m, is the primary unit of length in the International System of Units, though its prefixed forms are also used relatively frequently.
Number 6. Find the missing measure and round to nearest 10th
Note that Cosine law can be used if three sides of the triangle are given in order to get the angles.
For example, in getting the measurement of angle C
[tex]\cos C=\frac{a^2+b^2-c^2}{2ab}[/tex]Then take the arccos to get the angle C.
From the problem, we have :
We need to find the measurement of angle F using the same formula above.
[tex]\begin{gathered} \cos F=\frac{16^2+12^2-18^2}{2(16)(12)} \\ \cos F=\frac{19}{96} \end{gathered}[/tex]Taking the arc cosine :
[tex]\begin{gathered} \angle F=\arccos (\frac{19}{96}) \\ \angle F=78.58 \end{gathered}[/tex]The answer rounded to the nearest 10th is
Solve the trigonometric equation for all values 0 ≤ x < 2π.tan x - 1 = 0
What is the answer to this question?
The probability of drawing a blue socks and white socks is 1/12.
Given that, a drawer contains 10 red socks, 6 white socks and 8 blue socks.
What is probability of an event?Probability is a type of ratio where we compare how many times an outcome can occur compared to all possible outcomes.
As we know the probability of an event = Number of favorable outcomes/Total number of outcomes
Total number of outcomes = 10+6+8=24
Probability of getting blue socks = 8/24 = 1/3
Probability of getting white socks = 6/24 =1/4
Now, probability of an event = 1/3 × 1/4 = 1/12
Therefore, the probability of drawing a blue socks and white socks is 1/12.
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Victor earns 19% commission as a salesperson. He sold a microscope that cost $368.84. How much commission did Victor earn? Round your answer to the nearest cent: $
Victor earns 19% commission
He sold a microscope that cost $368.84.
so, the commission = 19% of $368.84 = 0.19 * 368.84 = 70.0796
Rounding to the nearest cent
So,
the commission = $70.08
7. 200 is the ? th term of 24, 35, 46, 57, ..
200 is the 17th term of the progression
What is arithmetic progression?
Arithmetic progression or arithmetic sequence (AP) is a numerical series in which the difference between subsequent terms is constant. The sequence 5, 7, 9, 11, 13, 15,..., for example, is an arithmetic progression with a common difference of 2. A finite arithmetic progression, or simply an arithmetic progression, is a finite section of an arithmetic progression. An arithmetic series is the sum of a finite arithmetic progression. An arithmetic series is the sum of the elements of a finite arithmetic progression. A closed expression determines the product of the members of a finite arithmetic progression with a beginning element a1, common differences d, and n elements in total.
This can be solved using arithmetic progression
Aₙ = a + (n - 1)d
where, Aₙ = 24, d = 35 - 24 = 11
so, n = (Aₙ - a)/d + 1 = (200-24)/11 + 1 = 17
Hence, 200 is the 17th term of the progression
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What is 3+2? and add 7 then subtract 4
the answer is 8
add 3+2, that gives u 5, add 7+5 which is 12, do 12-4 its equal to 8
What shape is generated when SABC is rotated around the vertical linethrough B and C?4ABA. PrismB. PyramidC. CylinderD. Cone
A triangle, when rotated about one of its sides will generate a solid in a form of a Cone.
The cone could be a hollow one or a solid-filled one, depending on the properties of the triangle being rotated.
Therefore, the shape generated is a cone.
Answer: D.
please help me work through this if you can, thank you!
Given:
[tex]C=\frac{x^4}{4}-\frac{4}{3}x^3-\frac{35}{2}x^2+150x[/tex]Let's solve for the following:
• (a). Find C'(x).
Here, we are to find the derivative of C(x).
Apply the sum rule:
[tex]\begin{gathered} C^{\prime}=\frac{d}{dx}(\frac{x^4}{4})+\frac{d}{dx}(-\frac{4}{3}x^3)+\frac{d}{dx}(-\frac{35}{2}x^2)+\frac{d}{dx}(150x) \\ \\ C^{\prime}=x^3-4x^2-35x+150 \end{gathered}[/tex]• (b). The critical numbers of C(x).
The critical numbers will be the points where the graph changes direction.
Using the derivative, let's solve for x.
[tex]x^3-4x^2-35x+150=0[/tex]Factor the left side using the rational root test:
[tex](x-5)(x^2+x-30)=0[/tex]Now factor using the AC method:
[tex]\begin{gathered} (x-5)((x-5)(x+6))=0 \\ \\ (x-5)(x-5)(x+6)=0 \end{gathered}[/tex]Equate each factor to zero and solve for x:
[tex]\begin{gathered} x-5=0 \\ \text{ Add 5 to both sides:} \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x-5=0 \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x+6=0 \\ x+6-6=0-6 \\ x=-6 \end{gathered}[/tex]Therefore, the critical numbers of C(x) are:
x = -6, 5
• (C). Increasing interval.
Use the critical points to find the increasing and decreasing intervals.
Using interval notation, the increasing interval is:
[tex](-6,5)\cup(5,\infty)[/tex]• D. Decreasing interval:
Using interval notation, the decreasing interval is:
[tex](-\infty,-6)[/tex]ANSWER:
(a). C'(x) = x³ - 4x² - 35x + 150
(b). x = -6, 5
(c). Increasing: (-6, 5) U (5,∞)
Decreasing: (-∞, -6)
The quadrilateral RSTU is inscribed in the circle shown below. S R U Jake wants to prove the theorem that says that the measure of the quadrilateral's opposite angles add to 180°. He knows that the measure of angle Ris half the measure of are STU and that the measure of angle T is half the measure of arc SRU. Which of the following is an appropriate step to prove that ZR + ZT =180°?
Arc STU and arc SRU can form the complete circle. Therefore
[tex]Therefore,[tex]\begin{gathered} 2R+2T=360^0 \\ \text{factorize left hand side} \\ 2(R+T)=360^0 \end{gathered}[/tex]Dividing both sides by 2, we have
[tex]Hence, the appropriate steps are: Assume that the measure of arcs STU and SRU add up to 360 degreesAlso, substitute 2 m
pick yes in options 2 and 3
pick no in options 1 and 4
Help need please!!!!!!!factorize 36a-12b-60c
Solution:
Given:
[tex]36a-12b-60c[/tex]The greatest common factor (GCF) is factored out of the expression.
The GCF is 12.
Hence,
[tex]36a-12b-60c=12(3a-b-5c)[/tex]Therefore, the factorization of the given polynomial 36a - 12b - 60c is;
[tex]12(3a-b-5c)[/tex]PLS HELP!!!!!
TRUE OR FALSE:
A single cube with a side of 1cm has the same surface-to-volume ratio as a structure containing 8 cubes with sides that equal 1cm (remember that surface of a cube with a side A is 6A2cm2 and the volume is A3cm3).
Answer:
the answer is true
Step-by-step explanation:
Write the value of 17 tens in three different ways. Use the largest unit possible.
Answer:
1 and 7 and 0
Step-by-step explanation:
What is the volume, in cubic inches, of a rectangular prism with a height of 19in, a width of 8in, and a length of 17in?
The volume of a rectangular prism is given by
[tex]V=L\times W\times H[/tex]Where L is the length, W is the width, and H is the height of the rectangular prism.
For the given case, we have
Length = 17 in
Width = 8 in
Height = 19 in
Let us substitute these values into the above formula
[tex]\begin{gathered} V=L\times W\times H \\ V=17\times8\times19 \\ V=2584\: in^3 \end{gathered}[/tex]Therefore, the volume of the given rectangular prism is 2584 cubic inches.