Final answer:
The actual distance between Madison and Centerville is calculated by multiplying the map distance by the scale factor. Madison and Centerville are 66 km apart in real life.
Explanation:
The actual distance between Madison and Centerville is calculated by multiplying the map distance by the scale factor:
Map distance = 6 cm
Scale factor = 1 cm : 11 km
Actual distance = 6 cm * 11 km = 66 km
Therefore, Madison and Centerville are 66 km apart in real life.
Find the slope of the line that passes through (-95, 31) and (-94, 6).
Answer:
The slope of the line that passes through (-95, 31) and (-94, 6) is -25.
Step-by-step explanation:
The equation of a line has the following format:
[tex]y = ax + b[/tex]
In which a is the slope.
Passes through the point (-95, 31).
When [tex]x = -95, y = 31[/tex]
[tex]y = ax + b[/tex]
[tex]31 = -95a + b[/tex]
Passes through the point (-94, 6).
When [tex]x = -94, y = 6[/tex]
[tex]y = ax + b[/tex]
[tex]6 = -94a + b[/tex]
We have to solve the following system:
[tex]31 = -95a + b[/tex]
[tex]6 = -94a + b[/tex]
We want to find a.
From the first equation
[tex]b = 31 + 95a[/tex]
Replacing in the second equation:
[tex]6 = -94a + 31 + 95a[/tex]
[tex]a = -25[/tex]
The slope of the line that passes through (-95, 31) and (-94, 6) is -25.
Cream filled chocolates are $3.59 a pound Billy bought 1/2 pound of vanilla creams what was the cost round your answer
A fourth as much as the product of two thirds and 0.8
A fourth as much as the product of two thirds and 0.8 is ²/₁₅
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem !
First, we will translate this word problem into a mathematical equation.
The product of two thirds and 0.8
[tex]\frac{2}{3} \times 0.8[/tex]
A fourth as much as the product of two thirds and 0.8
[tex]\frac{1}{4} (\frac{2}{3} \times 0.8)[/tex]
[tex]= \frac{1}{4} (\frac{2}{3} \times \frac{4}{5})[/tex]
[tex]= \frac{1}{4} (\frac{2 \times 4}{3 \times 5})[/tex]
[tex]= \frac{1}{4} (\frac{8}{15})[/tex]
[tex]= \frac{1}{4} \times \frac{8}{15}[/tex]
[tex]= \frac{1 \times 8}{4 \times 15}[/tex]
[tex]= \frac{8}{60}[/tex]
[tex]= \frac{8 \div 4}{60 \div 4}[/tex]
[tex]= \boxed {\frac{2}{15}}[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
Box i contains 4 red and 8 blue marbles while box ii contains 5 red and 3 blue marbles. an unfair coin is tossed –whose probability of turning up heads is 40%. if the coin comes up heads box i is chosen and a random marble is chosen, otherwise if it is tails the marble is chosen from box ii.(a)find the probability a red marble is chosen.(b)if a red marble is chosen, what is the probability it came from box i? (c)if a blue marble is chosen, what is the probability it came from box i?
The range of F(x) = 6 * 3x is all positive real numbers.
Tickets for the movies are $7 for adults and $4 for children. Fourteen people paid a total of $68 for tickets. How many were adults and how many were children?
Full-time ph.d. students receive an average of $12,837 per year with a standard deviation of $3000. find the probability that the average salary of a group of 16 randomly selected ph.d. students is more than $13,000.
Given a circle with a diameter of 4, which equation expresses π as the ratio of the circumference of a circle to its diameter?
C /4 = π
Took the test myself, this is the answer.
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number?
The answer is 0.5.
To find the answer, understand the place value system in numbers.
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number.
To find the answer, we need to understand the place value system. In the number 653,841, the digit in the hundreds place is 8, and the digit in the thousands place is 5. Therefore, 1/10 of the digit in the thousands place is 0.5.
So, the answer is 0.5.
How to find the area under the standard normal curve between z 1.5 and z 2.5?
We have that for the Question, it can be said that the area under the standard normal curve between z 1.5 and z 2.5 is
P(1.5 &2.5) =0.06
From the question we are told
How to find the area under the standard normal curve between z 1.5 and z 2.5?
Generally the equation for the probability is mathematically given as
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
Where
P(Z < 2.5) = 0.99
P(Z < 1.5) = 0.93
From Z Table
Therefore
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
P(1.5 &2.5) =0.06
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Which multiplication expression that does not belong based on scaling. Explain.
Choose an expression
6 x 2 1/2
6 x 3 3/5
1/2 x 6
2 2/5 x 6
4x. (2x^3 — x^2–18x+15) Standard Form
Jack purchased a box of 1,000 candy guitar lollipops to sell in the bakery for $20.00. How much did he pay for each lollipop?
Describe the test grades using the measures of center
A pendulum travels 30 inches on its first swing. During each of its subsequent swings, it travels 90 percent of the previous swing.
Answer:
a1= 30 and r=0.9
Step-by-step explanation:
edge
Jeannie's restaurant served 58 customers on Monday. After the first day the amount of customers served decreases at a rate of 2.5% each day.
What is the explicit rule for this situation and approximately how many customers will be served on the 6th day?
Round to the nearest customer.
Drag and drop the answers into the boxes to match the situation.
Explicit rule
Number of customers on the 6th day.
A n = 58 x (0.975) n - 1, A n = 58 x (0.025) n - 1, A n = 58 (1.025) n - 1, 51, 49, 48, 46,
Answer:
51 customers
Step-by-step explanation:
Jeannie's restaurant served 58 customers on Monday.
Rate of decrement r =2.5 % = 0.025
Formula : [tex]y=a(1-r)^{n-1}[/tex]
A is the initial amount
r is the rate
n is the no. of days
So, Substitute the values
[tex]y=58(1-0.025)^{n-1}[/tex]
[tex]y=58(0.975)^{n-1}[/tex]
So, explicit rule : [tex]A_n=58(0.975)^{n-1][/tex]
Now to find the no. of customers will be served on the 6th day
Substitute n = 6
[tex]A_6=58(0.975)^{6-1}[/tex]
[tex]A_6=51.1035[/tex]
So, 51 customers will be served on the 6th day
Cheryl paid $3.00 for a pair of socks and eight times as much for a pair of shoes. Her brother Kevin also bought socks and shoes but paid twice as much as Cheryl did for each. How much money did they spend together ?
in fifteen minutes greg sailboat went 3/6 miles, gina sailboat went 6/6 miles, and stuart sailboat went 4/6 miles. whose sailboat went the longest distance in fifteen minutes?
Find the fifth term of A n = 2n
if c is the incenter of AMD, AMC=3x+6 AND dmc = 8X-49, FIND EACH MEASURE
Answer:
[tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].
Step-by-step explanation:
As you can observe in the image attached, angles AMC and DMC are congruent, because if point C is the incenter of AMD, that means each line the forms such point is a bisector.
Remember that a bisector is a line that equally divides an angle.
So,
[tex]\angle AMC = \angle DMC\\3x+6=8x-49[/tex]
Solving for [tex]x[/tex], we have
[tex]6+49=8x-3x\\5x=55\\x=11[/tex]
Then, we substitute this value in each expression to find the angles.
[tex]\angle AMC = 3x+6 = 3(11)+6=33+6=39[/tex]
[tex]\angle DMC = 8(11)-49=88-49=39[/tex]
Therefore, the measures of those angles are [tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].
Choose the graph that represents the time for which the velocity of the ball will be between –90 and –58 ft/s.
The answer is c because t must be less than 2.5 and more than 1.5.
Find this by separating the inequality into:
-90 < -32t - 10
&
-32t - 10 < -58
Simplify and you get 2.5 and 1.5
Graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
We have:
The velocity of the ball will be between –90 and –58 ft/s.
Let v be the velocity of the ball:
v lies between -90 and -58
-90 < v < -58
The above expression represents the inequality:
Or
-90 < -32t - 10
t < 2.5
And
-32t - 10 < -58
t > 1.5
The number line will be:
Open the circle on the number 1.5 and open circle at 2.5 and a line was drawn between this point.
Thus, graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
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Use the diagram of the right triangle above and round your answer to the nearest hundredth. If m
Answer choices:
A) 17.32 m
B) 6.83 m
C) 14 m
D) 9.99 m
Answer:
b. 6.93 m.
Step-by-step explanation:
We have been given triangle ABC and we are asked to find the measure of a.
We will use law of sines to solve our given problem.
[tex]\frac{a}{\text{Sin}(A)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are opposite sides of angle A, B and C respectively.
First of all, we will find the measure of angle B using angle sum property.
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]30^{\circ}+\angle B+90^{\circ}=180^{\circ}[/tex]
[tex]\angle B+120^{\circ}=180^{\circ}[/tex]
[tex]\angle B=180^{\circ}-120^{\circ}[/tex]
[tex]\angle B=60^{\circ}[/tex]
Upon substituting our given values in law of sines we will get,
[tex]\frac{a}{\text{Sin}(30^{\circ})}=\frac{12}{\text{Sin}(60^{\circ})}[/tex]
[tex]\frac{a}{0.5}=\frac{12}{\frac{\sqrt{3}}{2}}[/tex]
[tex]\frac{a}{0.5}=\frac{2*12}{\sqrt{3}}[/tex]
[tex]\frac{a}{0.5}*0.5=\frac{24}{\sqrt{3}}*0.5[/tex]
[tex]a=\frac{12}{\sqrt{3}}[/tex]
[tex]a=6.9282032302755\approx 6.93[/tex]
Therefore, the value of a is 6.93 meters and option 'b' is the correct choice.
In a line of students ,Jenna is number 8.The teacher says the rule for a number pattern is add4.The first term 7.What number should Jenna say?
Two rectangular prisms have the same volume. The area of the base of the blue prism is 216 square units. The area of the base of the red prism is one third that of the blue prism. Which statement is true?
a) The height of the red prism is one-third the height of the blue prism.
b) The height of the red prism is the same as the height of the blue prism.
c) The height of the red prism is six times the height of the blue prism.
d) The height of the red prism is three times the height of the blue prism.
Answer:
D
Step-by-step explanation:
This list shows the age at which 43 U.S. Presidents began their terms. 57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46 Before you can make a frequency table, you need to decide how to set up the age intervals. What is the BEST way to group these ages into six intervals?
The best way to group these ages into six intervals is from 40-44 to 65-69.
What is a Frequency Distribution Table ?A frequency distribution table gives an idea about the data point or interval and its frequency.
The age of the Presidents given as
57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46
The smallest number ( age) is 42 and the largest number (age ) is 69
To make 6 intervals in this gap of 27 , each interval should be of length 5
Therefore the intervals will be
40-44
45-49
50-54
55-59
60-64
65-69
This is the best way to group into intervals.
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Final answer:
The best way to group the ages of U.S. Presidents into six intervals for a frequency table is by intervals of five years each, starting at age 42 and ending at age 71, to cover the entire range and maintain equal width for all intervals.
Explanation:
When grouping ages into intervals for a frequency table, it's best to have intervals that are of equal width and cover the entire range of data without overlap. For the ages of U.S. Presidents starting their terms, which range from 42 to 69, we could divide this range into six intervals in a way that makes sense for this data set.
First, find the range by subtracting the youngest age from the oldest: 69 - 42 = 27. Next, divide this range by the number of desired intervals (6), which gives us 4.5. We can round this to 5 to make the intervals more practical. Thus, each age interval will span 5 years. Starting at 42, the six intervals would be: 42-46, 47-51, 52-56, 57-61, 62-66, and 67-71.
This grouping covers all the ages and each interval is of equal width, making it easy to interpret the frequency table.
y = -16x2 + 32x - 10 This parabola has x-intercepts, representing the times when the dolphin's height above water is feet.
Answer:
2
0
two real solutions
Step-by-step explanation:
from edge!!
To find the x-intercepts of the quadratic equation representing the height of a dolphin's jump, we can use the quadratic formula by plugging in the coefficients from the equation y = -16x^2 + 32x - 10. The intercepts indicate the times when the dolphin's height above water is zero feet.
Explanation:The question involves finding the x-intercepts of a quadratic equation, which represent the points where a parabola crosses the x-axis. In this context, the x-intercepts correspond to the times when the dolphin's height above water is 0 feet. To find the x-intercepts, we can use the quadratic formula:
x = −b ± √(b² − 4ac) / (2a)
For the equation y = −16x² + 32x − 10, the coefficients are a = −16, b = 32, and c = −10. By substituting these values into the quadratic formula, we can calculate the times when the dolphin is at the water level (y=0). Since this is a mathematical problem involving a real-world scenario, it is essential to check that the resulting times make sense within the context. Negative values for time, for example, would not be physically meaningful.
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8pints compared to 15 cups
find the domain of
[tex]f(x) = \frac{ \sqrt{x + 2} }{ {x}^{2} - 25 } [/tex]
Write the epxressions for the equivalent capacitance of two capacitors write your answers in terms of c1 and c2
What is 30 divided by half plus 10