The actual distance between the cities are 40 miles.
What is the scale factor?The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.
According to the question we are given that On a map, 1 inch equals 5 miles. two cities are 8 inches apart on the map.
that is, 1cm : 5 miles
Here two cities are 8 inches apart on the map.
then 8 inches equals to
5 x 8 = 40 miles.
The actual distance is 40 miles.
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Of five letters (a, b, c, d, and e), two letters are to be selected at random. how many possible selections are there
The lengths of the sides of a right triangle are a and b, and the hypotenuse is
c. find the area of the triangle. a=2 squareroot 3; c=4 a = sq. ft.
Answer:
Area is 2√3 ft².
Step-by-step explanation:
Given,
A right triangle having sides,
a = 2√3 ft,
c = 4 ft,
Where, c is the hypotenuse of the triangle,
If b is the other leg of the triangle,
By the pythagorean theorem,
[tex]c^2=a^2+b^2[/tex]
[tex]4^2=(2\sqrt{3})^2+b^2[/tex]
[tex]16=12+b^2[/tex]
[tex]4=b^2[/tex]
[tex]\implies b = 2[/tex]
Hence, the area of the given triangle is,
[tex]A=\frac{1}{2}\times a\times b[/tex]
[tex]=\frac{1}{2}\times 2\sqrt{3}\times 2[/tex]
[tex]=\frac{4\sqrt{3}}{2}[/tex]
[tex]=2\sqrt{3}\text{ square ft}[/tex]
Write the sum using summation notation, assuming the suggested pattern continues.
2 - 12 + 72 - 432 + ...
Answer:
[tex]\displaystyle \sum_{k=1}^{n}2(-6)^{k-1}[/tex]
Step-by-step explanation:
we have to write the sum using summation notation of the following series:
2-12+72-432+...
which could also be written as:
2+(-12)+72+(-432)+...
We observe that first term=2
second term=2×-6
Third term=2×-6×-6
Fourth term=2×-6×-6×-6
nth term=[tex]2\times (-6)^{n-1}[/tex]
Hence, the series sum= [tex]\displaystyle \sum_{k=1}^{n}2(-6)^{k-1}[/tex]
1. A ladybug lands on the end of a pinwheel that is spinning at a steady speed. The equation y = –7 sin (0.4πx) + 11 gives the height of the ladybug y, in centimeters, above the ground x seconds after landing. What is the diameter of the pinwheel
The shoe store has twice as many black shoes as it does brown shoes. The total number of shoes is 66. How many brown shoes are there?
To solve the problem, denote the number of brown shoes as x, and the black shoes as 2x, as the store has twice as many black shoes. The total number of shoes is x + 2x = 66. Solving this gives us x (brown shoes) as 22.
Explanation:The subject is concerning a mathematical problem involving ratios. In the given problem, it is stated that the shoe store has twice as many black shoes as brown shoes, and the total number of shoes is 66. Here's a step-by-step process to solve it:
Let's denote the number of brown shoes as x. Therefore, due to the problem stating that there are twice as many black shoes, the number of black shoes will be 2x.The total number of shoes is the sum of the brown shoes (x) and the black shoes (2x), thus the equation becomes: x + 2x = 66.Solving this equation gives us:3x = 66.Divide both sides of the equation by 3 to isolate x, which gives us x = 22.Therefore, there are 22 brown shoes in the store.
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________ probability is used when we know the number of possible outcomes of the event of interest and the total number of possible outcomes in the sample space.
Assume the birth of a boy or a girl is equally likely. The probability that a single child is born a girl is 1/2. What is the probability that the next child born to the same familiy will also be a girl?
probability is 1/4 (b)
Step-by-step explanation:
Which expression can be written as x + 4 = x^2? Assume x > 0
DATA MANAGEMENT GRADE 12! HELP
Between periods at a hockey game, some fans are selected to shoot a puck at the net from each of 10 m, 15 m and 30 m, with winnings of $50, $100 and $1000 per goal scored, respectively. The chance of scoring from each position has been estimated to be 60%, 20% and 2%, respectively. What is the expected payout per fan? Question 6 options: $140 $70 $2300 $26 620
50 POINTS!!!!!!!!!
Find a number that is between 7/11 and 0.75, theres a line on top of 75
77/99
23/33
25/44
76/99
To convert 0.9 to a fraction, Lauren wrote n=0.9 as her first step. For her second step, what should she multiply both sides of that equation by?
10
100
1000
10000
Which number is between 1/7 and 0.2 ?
9/35
6/35
2/9
1/9
Which fraction shows 5.2 as the quotient of two integers?
11/2
21/5
26/5
51/10
What can you say about the nature of any other zeros of the quadratic equation which has one complex zero? Explain your answer.
If a car is $27,000 and loses 15% of its value each year what will be the value in 5 years
(05.05)On the coordinate plane below, what is the length of AB?
A coordinate plane is shown with the following points A at negative 9, 4; B at 5, 4; C at 5, negative 5; D at negative 9, negative 5. All points are connected to create a rectangle.
8 units
9 units
14 units
15 units
Answer:
14 units
Step-by-step explanation:
both points have the same y-coordinate, so therefore, the line is horizontal from x = -9 and x = 5 9 (plus I did the 5.05 math quiz segment two 6th grade)
How do you solve equations for indicated variables?
ax+r=7
Solving for x?
The solution is x = (7 - r) / a.
To solve the equation ax + r = 7 for x, follow these steps:
Subtract r from both sides of the equation:
ax + r - r = 7 - r
This simplifies to:
ax = 7 - r
Divide both sides by a:
x = (7 - r) / a
Substitute the value of x back into the original equation to ensure it is correct.
Which is an undefined term that is useful for defining a circle?
a. angle
b. distance
c. line
d. segment
given that (6,-8) is on graph f(x), find the corresponding point for the function f(-1/2x)
A spherical scoop of ice cream is placed on top of a hollow ice cream cone. the scoop and cone have the same radius. the ice cream melts completely and it fills the cone to the top. how many times greater is the height of the cone than the radius of the cone?
K is the midpoint of line segment lm. the coordinates of k are (5, 12) and the coordinates of l are (2, 6), find the coordinates of m.
What is the answer to this?
Write the equation in vertex form
f (x)= x^2-10x+16
URGENT!!
what is this graph considered:
A: Bimodal Skewed
B: Bimodal Symmetric
C: Unimodal Skewed
D:Uniform
E: Unimodal Symmetric
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. −6y2 − 9y = −1
Which expression gives the same result as ∑4i=0(5)(1/3)i?
The symbol, ∑ is a summation sign that drills us to sum the elements of a sequence. The variable of summation is represented by an index that is placed under the summation sign and is often embodied by i. The index is always equal to 1 and adopt values beginning with the value on the right hand side of the equation and finishing it with the value over head the summation sign. So in the expression ∑4i = 0(5)(1/3)i will be the same as:
∑4i = 0(5)(1/3)i
= (1/3)⁰ + (1/3)¹ + (1/3)² + (1/3)³ + (1/3)⁴ + (1/3)⁵
= 364/243
Use the pythagorean theorem to find the distance between x(7,11) and y(-1,5)..
Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y. Which two figures have the same volume?
Choices:
Prism M
Cylinder p
Cone Z
And
Pyramid N
Prism Q
Cylinder Y
The measure of an angle is 60° less than nineteen times the measure of its supplement. what is the measure of the angle?
The measure of the angle will be;
⇒ 60°
What is Supplementary angle?The sum of two or more angle is 180 degree then the angle is called the Supplementary angle.
Given that;
The statement is,
''The measure of an angle is 60° less than nineteen times the measure of its supplement.''
Let measure of an angle = x
So, The measure of its supplement = 180° - x
Hence, We can formulate;
⇒ x = (180 - x) - 60°
Solve for x as;
⇒ x = 180 - x - 60
⇒ x + x = 120
⇒ 2x = 120
⇒ x = 120/2
⇒ x = 60°
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20 POINTS
Robinson's home run hitting distance is normally distributed with a mean of 394 feet and a standard deviation of 35 feet. He wanted to find the probability that his home runs traveled at least 380 feet. He calculated the z-score to be −0.40 and looked up the probability on the Standard Normal Probabilities table. He found that the table stated his probability as 0.3446. Determine whether Robinson made an error in his calculation and explain.
I need step by step instructions
Answer:
he made an error, the probability that his homeruns traveled at least 380 feet is 65.54%
Step-by-step explanation:
let´s see the Robinson's calculation:
using the formula for normal distribution:
Z = (x-μ)(σ/[tex]\sqrt{n}[/tex]) [1]
where:
x is raw measurement
μ is the mean
σ is the standar deviation
n is the size of sample
in this case x = 380, μ = 394, σ = 35, n = 1.
then using the equation [1] he calculated the Z score:
[tex]Z = \frac{380-394}{\frac{35}{\sqrt{1}}}\\\\Z = -\frac{14}{35}\\\\Z = -0.4\\\\[/tex]
and it's correct but his answer is wrong because he confuse the term at least.
at least means that the probability be greater than 380 feet, not less than 380 feet.
so he looked the Z score in a table of normal distribution (this table has been attached) and effectively this value is 0.3446. but as I told you this probability is for x < 380.
therefore, the probability that his homeruns traveled at least 380 feet is:
[tex]P(x > 380) = 1 - P(x < 380)\\\\P(x > 380) = 1 - 0.3446\\\\P(x > 380) = 0.6554 \ or \ 65.54 \%[/tex]
please see the table attached.
Kite DCFE is inscribed in circle A shown below:
If the measure of arc DEF is 266°, what is the measure of ∠DEF?
Numerical Answers Expected!
Answer:
133 degrees
Step-by-step explanation:
Given is a picture of a kite DCFE inscribed in circle A
The vertices of the kite D, C, E and F lie on the circle.
A is the centre.
Arc DEF = 266 degrees
This means the subtended angle of arc DEF at the centre = Angle DAF = 266
By theorem on circles, we have central angle of any arc is twice the angle subtended by the arc on the remaining part of the circumference
Hence
Angle DEF = 1/2 angle DAF
i.e. DEF =[tex]\frac{266}{2} =133[/tex]
133 degrees
The distance between points (3, 7) and (x1, y1) is the square root of (x1 - 3)2 + (y1 - 7)2. True or false?
Answer:
True
Step-by-step explanation:
By the distance formula,
The distance between two points [tex](a_1, b_1)[/tex] and [tex](a_2, b_2)[/tex] is,
[tex]d=\sqrt{(a_2-a_1)^2+(b_2-b_1)^2}[/tex]
Here, [tex]a_1=3[/tex], [tex]b_1=7[/tex], [tex]a_2=x_1[/tex] and [tex]b_2=y_1[/tex]
Thus, the distance would be,
[tex]d=\sqrt{(x_1-3)^2+(y_1-7)^2}[/tex]
= the square root of [tex](x_1 - 3)^2 + (y_1 - 7)^2[/tex]
A junior basketball has a diameter of approximately 7 in., and a regulation basketball has a diameter of approximately 9.5 in. about how many times as great is the volume of the regulation basketball as the volume of the junior basketball?