The shadow of the 4 feet stick is 3/4 feet or 0.75 feet.
It is a question of ratio and proportion.
It is given in the question that the 32 feet tall building had a shadow 6 feet long.
We have to find the length of the shadow of a 4 ft stick.
Let the length of the shadow of a 4 ft stick be x.
We know that length and shadow of a 4 feet stick and a 32 feet building will be in proportion.
Hence, we can write,
Length of building/Length of stick = shadow of building/shadow of stick
32/4 = 6/x
8 = 6/x
x = 6/8 feet = 3/4 feet = 0.75 feet
x = 0.75 feet.
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In a standard normal distribution, the range of values of z is from _____.
In a standard normal distribution, the range of values of z is from: D. d. -∞ to ∞.
What is a z-score?A z-score is also known as a standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
What is a normal distribution?A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than the data that are far from the mean.
In conclusion, the range of values of z in a standard normal distribution are all real numbers which typically ranges from negative infinity (-∞) to positive infinity (∞).
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Complete Question:
In a standard normal distribution, the range of values of z is from ______.
a. -3.09 to 3.09
b. -1 to 1
c. 0 to 1
d. -∞ to ∞
X+4y=10 and 3x-y=-9 find the value of x/y
[tex]x = 10 - 4y.....(3)[/tex]
I WILL SOVE BY SUBSTITUTION.
[tex]3(10 - 4y) - y = - 9 \\ 30 - 12y - y = - 9 \\ - 13y = -9 - 30 \\ - 13y = - 39 \\ \frac{ - 13y}{ - 13} = \frac{ - 39}{ - 13} \\ y = 3 \\ [/tex]
[tex] x= 10 - 4(3) \\ x = 10 - 12 \\ x = - 2[/tex]
we have (-2,3)
ATTACHED IS THE SOLUTION
The Stingrays at the zoo requires the 196 gallon tank to be 4% salt. After a period of time, some water evaporated, raising the salinity to 7%.
How many gallons of water must be resupplied in order to bring the salinity back down to 4%?
Answer:
196 x 3 / 100 = 5,88
Step-by-step explanation:
7% - 4% = 3%
So we need to had 3% t have again 4%
18 is 50% of what????????
Let the unknown value be x.
18 is 50% of ________n can also be written as;
18 = 50% of x
of means multiplication;
18 = 50% * x
18 = 50/100 * x
18 = 50x/100
cross multiply
18 * 100 = 50x
1800 = 50x
Divide both sides by 50
1800/50 = 50x/50
180/5 = x
x = 180/5
x = 36
Hence 18 is 50% of 36
Which of the following equations best represents "y is inversely related to x"?
y = kx
y = kx2
y = k(1/x)
y = k(1/x2)
and i dont think it is c
The equations best represents "y is inversely related to x" is y = k(1/x).
What is an inverse proportionality?The inverse proportionality can be described as the relationship that exist between two or more quantities whereby when one of the quantities is increasing in value, then the the second quantity will be decreasing in value however there will be a proportionality constant that would be found in the equation.
Considering the chosen option D, we can see that when the value of y is increasing then the value of x will be decreasing, and when the value of x is decreasing , them the value of y will be increasing.
Therefore, option C is correct.
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=
O DECIMALS, PROPORTIONS, PERCENTS
Simplifying a ratio of whole numbers: Problem type 1
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
40 L: 72 L
Answer:
5/9
Step-by-step explanation:
You want the reduced fraction equivalent to the ratio 40L : 72L.
Reduced ratioA ratio is reduced by removing the greatest common factor from all parts of the ratio. Here, that factor is 8L.
40L : 72L = (8L)(5) : (8L)(9) = 5 : 9 = 5/9
The ratio is 5/9.
__
Additional comment
The greatest common factor can be found several ways. The easiest is for you to make use of your knowledge of multiplication tables:
40 = 5·8
72 = 9·8
8 is a common factor. Since 5 and 9 have no common factors, 8 is the greatest common factor of 40 and 72.
Which of the following ordered pairs is either the
x- or y-intercept of the function 3x + 2y = -6?
A. (-3,0)
B.(-2,0)
C.(0,2)
D.(0,3)
Please help me with this question
Notice from the graph that data are mostly to the right.
Answer: Option C The distribution is tailed.
Help
Simplify the negative exponent. Please show your work.
4 ⁻⁴
Answer: 0.0625
Step-by-Step Explanation: positive exponents = multiply the number by itself however many times the exponent demands.
negative exponents: multiply the reciprocal of the base number by itself however many times the exponent demands.
Find the measure of arc indicated using the inscribed angle given in thecircle below.X91 0YZ?
SOLUTION
The correct option is A (the first option)
We are asked to find the measure of the angle at the center.
Circle theorem:
The angle at the center of a circle = 2 x Angle at the circumference
The angle at the center of the circle = 2 x = 2 x 91 degrees
=182 degrees
The value for the angle at the center (?) of this circle is
[tex]182^o[/tex]The correct option is A (the first option)
Heights of 10-year old's, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches.
(a). The height requirement for Batman the Ride is 54 inches. What percent of 10 year old's cannot go on this ride?
(b). Suppose there are four ten year olds. What is the chance that at least two of them will be able to ride Batman the Ride?
(c). Suppose you work at the park to help them better understand their customers demoghraphics, and you are counting people as they enter the park. What is the chance that the first 10 year old you see who can ride Batman the Ride is the 3rd 10 year old who enters the park?
(d). What is the chance that the 5th 10 year old you see who can ride Batman the Ride is the 12th 10 year old who enters the park?
Using the normal distribution and the binomial distribution, it is found that:
a) 43.25% of 10 year old's cannot go on this ride.
b) There is a 0.7814 = 78.14% probability that at least two of them will be able to ride Batman the Ride.
c) There is a 0.1062 = 10.62% probability that the first 10 year old you see who can ride Batman the Ride is the 3rd 10 year old who enters the park.
d) There is a 0.0834 = 8.34% probability that the 5th 10 year old you see who can ride Batman the Ride is the 12th 10 year old who enters the park.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.In the context of this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 55, \sigma = 6[/tex]
For item a, the proportion is the p-value of Z when X = 54, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (54 - 55)/6
Z = -0.17.
Z = -0.17 has a p-value of 0.4325.
Hence the percentage is of 43.25%.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.For item b, the parameters of the binomial distribution are given as follows:
p = 0.5675, n = 4.
Hence:
P(X = 2) = 6 x (0.5675)² x (0.4325)² = 0.3615.P(X = 3) = 4 x (0.5675)³ x (0.4325)¹ = 0.3162.P(X = 4) = (0.5675)^4 = 0.1037.Hence:
P(X >= 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.3615 + 0.3162 + 0.1037 = 0.7814.
Which is the probability.
For item c, the probability is given as follows:
p x P(X = 0 with n = 2).
Hence:
p = 0.5675 x (0.4325)² = 0.1062.
For item d, the probability is given as follows:
p x P(X = 4 with n = 11). (inverse binomial).
Hence:
0.5675 x (11!)/(5! x 6!) x (0.5675)^4 x (0.4375)^7 = 0.0834.
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Determine whether the mean, median, or mode would be the best choice to describe the center of the following set of data.
An elementary school has 92 first graders. Because the first graders are all about the same age, they have heights that are pretty similar to one another.
Would it be best to use the mean, median, or mode to describe the height of the first-graders?
Group of answer choices
Mean
Median
Mo
First graders in an elementary school number 92. We use mode.
Given that,
Determine which statistic would be most appropriate to characterize the middle of the next set of data: the mean, median, or mode.
First graders in an elementary school number 92. The first graders' heights are fairly similar to one another because they are all roughly the same age.
We have to find which statistic—the mean, median, or mode—does the first-graders' height best represent.
First graders in an elementary school number 92.
Depending on which their birthday walls, the first graders might be six, seven and eight on the last day of the second year.
Therefore, We use mode.
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13. Making an argument. Your friend claims that a line always represents a function. Is your friend
correct? Explain your reasoning
Based on the given argument, it is concluded that my friend's reasoning was incorrect.
What is a Linear Function?This refers to the type of function that represents one line on a linear plane in cartesian mathematics.
With this in mind and from the claim of my friend that a line always represents a function, my friend is incorrect because If the line was vertical, then it could not pass through and as such, cannot represent a function.
Therefore, the answer to the question is that my friend is incorrect in his claim about lines and functions.
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The proof is converted to paragraph form.
Which parts of the paragraph proof are incorrect?
The part "since ∠ AMC is a right angle, ∠BMC and ∠CMD will be complementary" and "since ∠ BMC is a right angle, ∠BMC and ∠AMB will be complementary" , the paragraph proof is incorrect.
We are given that,
∠ AMC and ∠BMC are right angles.
Since,
∠ AMC = ∠ AMB + ∠ BMC
The paragraph part should have been ∠ AMB and ∠ BMC are complementary angles and,
Since,
∠ BMD = ∠ BMC + ∠ CMD
The paragraph part should have been ∠ CMD and ∠ BMC are complementary angles instead of the part given in the paragraph proof.
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Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function
The definition of the functions implies that the value of x if f(x) = g(x) is 3
The solution for the value of xThe equations of the functions are given as
f(x) = -2x + 4
g(x) = 2x - 8
This means that, we have the following equation
f(x) = g(x)
Substitute the known values in the above equation
So, we have the following equation
-2x + 4 = 2x - 8
Collect the like terms in the above equation
So, we have
2x + 2x = 8 + 4
Evaluate the like terms in the above equation
So, we have
4x = 12
Divide both sides by 4
x = 3
Hence, the value of x such that the equations are equal is 3
The graph of the functionsThe graph of the functions can be plotted using a graphing tool
See attachment for the graph of the functions
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Rhianna drew a scale drawing of a house and its lot. She used the scale 9 inches = 5 feet. What is the scale factor of the drawing?
Simplify your answer and write it as a fraction.
The scale factor that was used for the drawing is 1 inch represents [tex]\frac{5}{9}[/tex] feet.
What is the scale factor?A fraction is a non-integer that has a numerator and a denominator. An example of a fraction is 2/9. 2 is the numerator and 9 is the denominator.
A scale drawing is either a smaller or a bigger version of another image. If the scale used in the drawing is smaller in relation to the dimension of the original image, the scale drawing is a reduced image. If this is not the case, then it is a bigger scale drawing.
The scale drawing is usually reduced at a constant dimensions using a scale factor. In order to determine the scale factor, divide both dimensions provided by 9.
(9 / 9) = (5 / 9)
1 inch = 5/9 feet
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Shauna calculated the net sales for her company using the following figures: Gross sales = $72,900 Sales discounts = $2,450 Purchase returns and allowances = $3,750 Sales returns and allowances = $2,550 The net sales of Shauna's company are __________.
The net sales of Shauna's company when she calculated the sales for her company using the figures is $66700.
What are net sales?The total of a company's net sales is its gross sales less any returns, allowances, and discounts. Externally, net sales calculations are not always obvious. They can frequently be taken into account when calculating top-line revenues that are shown on the income statement.
The total number of units sold is multiplied by the price per unit for the purpose of calculating gross sales. The term "returns" or "sales returns" refers to products that customers have sent back in exchange for reimbursement.
The nets sales based on the information given will be:
Gross sales = $72900
Less: Retuned sales = $3750
Less Discount = $2450
Net sales = $66700
Therefore, the net sale is $66700.
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Write an equation in standard form for the line that passes through the given points.
(5,0) and (0,3)
The equation of the line in standard form is
(Type your answer in standard form.)
3x + 5y = 15 is the equation of the line in standard form that passes through the point (5,0) and (0,3).
What is the equation of line that passes through the given points?The formula for equation of line is expressed as;
y = mx + b
Where m is the slope and b is the y-intercept.
Given the data in the question;
Point 1 ( 5,0 )
x₁ = 5y₁ = 0Point 2 ( 0,3 )
x₂ = 0y₂ = 3First, we determine the slope of the line.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 3 - 0 )/( 0 - 5 )
Slope m = ( 3 )/( -5 )
Slope m = -3/5
Now, we plug the slope and coordinates of one the point into the equation of line to determine the y-intercept b.
y = mx + b
0 = (-3/5)5 + b
Solve for b
0 = -15/5 + b
0 = -3 + b
b = 3
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (-3/5)x + 3
Convert to standard form; Ax + Bx = C
Multiply each term by 5
y = (-3/5)x + 3
5y = 5(-3/5)x + 5(3)
5y = -3x + 15
Reorder the equation
3x + 5y = 15
Therefore, the equation of the line is in standard form is 3x + 5y = 15.
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A zookeeper is 6 14 feet tall. A young giraffe in his care is 93/8 feet tall. How many times as tall as the zookeeper is the giraffe?
I need help with this
Answer:
[tex]\text{ 78 miles per hour}[/tex]Step-by-step explanation:
Given the linear function for the traffic fines:
[tex]f(s)=14(s-60)+40[/tex]If a fine comes to $292, substitute f(s)=292 and solve for "s" to find the speed of the person:
[tex]\begin{gathered} 292=14(s-60)+40 \\ 292=14s-840+40 \\ 14s=292+840-40 \\ 14s=1092 \\ s=\frac{1092}{14} \\ s=78\text{ miles per hour} \end{gathered}[/tex]Use the square root property to solve the equation.(x + 8)² = 2Select one:O A. (-8+√√2)OB. √2-√√8O C. (√2+8,-√2+8}O D. (-8± √2)
Answer: D
Solve similar triangles (advanced) khan academy. solve for x
Answer:
that would be X=22, i had the same thing today, and got it right :D
Step-by-step explanation:
The sum of a number and 4
The solution for x in the equation x + 4 = 12 is 8.
Given,
Sum of two numbers is 12
Take the first number as x
Second number is given as 4
We have to find the value of x.
The equation will be like:
x + 4 = 12
Solve for x in the equation.
Add -4 to both sides
x + 4 - 4 = 12 - 4
x = 8
That is, the solution for x in the equation x + 4 = 12 is 8.
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The question is incomplete. Completed question is given below.
The sum of a number and 4 is 12. Find the number.
A pedestrian signal at a crosswalk has the following cycle: "WALK” for 45 seconds, "DON'TSTART" for 30 seconds and "DONT WALK" for 40 seconds. What is the probability the signalwill show "DON'T START" if you arrive at a random time? Write your answer as a percentagerounded to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
The probability is represented by the following equation:
[tex]undefined[/tex]convert 0.43 to a percent
Answer:
43%
Step-by-step explanation:
To convert a decimal to a percent, you have to move the decimal over 2 times to the right.
Where do you find a vertical shift in the exponential parent function?
What happens when (x-4) is in the exponent?
What happens when (x+9) is in the exponent?
Where do you find a horizontal shift in the exponential parent function?
What happens when there is a +7 at the end of the exponential parent function?
What happens when there is a -6 at the end of the exponential parent function?
For the given expressions we will have:
y = exp(x - 4) →we have a shift of 4 units to the right.
y = exp (x +9) → we have a shift of 9 units to the left.
y = exp(x) + 7 → we have a shift of 7 units up.
y = exp(x) - 6 → we have a shift of 6 units down.
How to work with vertical and horizontal shifts?
Remember that the shifts work as follows.
For a function f(x), we define a vertical shift of N units as:
g(x) = f(x) + N
If N > 0, the shift is upwards.If N < 0, the shift is downwards.For a function f(x), we define a horizontal shift of N units as:
g(x) = f(x + N)
If N > 0, the shift is to the left.If N < 0, the shift is to the right.Then, if we have:
exp(x - 4) we have a shift of 4 units to the right.
exp (x +9) we have a shift of 9 units to the left.
exp(x) + 7 we have a shift of 7 units up.
exp(x) - 6 we have a shift of 6 units down.
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Volume is 10x3 + 67x2 + 30x − 72, length is 5x − 4, width is 2x + 3
Answer:
height = x + 6
Step-by-step explanation:
Volume = length x width x height
V = 10x³ + 67x² + 30x − 72
length = 5x - 4 and width = 2x + 3
So length x width = (5x - 4 ) x (2x + 3)
Using the FOIL method:
= (5x)(2x) + (5x)(3) + (-4)(2x) + (-4)(3)
= 10x² + 15x - 8x - 12
= 10x² + 7x -12
So to find height, divide Volume by (length x width)
10x³ + 67x² + 30x − 72 ÷ 10x² + 7x -12
Use polynomial long division. See image ( I did the best I could to capture the process)
The answer is x + 6
To verify
Multiply (5x-4) (2x + 3) (x + 6) = 10x³ + 67x² + 30x − 72
someone help please, dk what to do
Step-by-step explanation:
equation format: y = mx + b where m is slope and b is the y intercept.
From the points given we find that it is a horizontal line, which means slope or m = 0. So we know so far:
y = 0x + b or y = b
The y-intercept occurs where x = 0. This occurs at y = -7. So the equation for these two points:
EQUATION: y = -7
(Plotted graph attached)
The length of a rectangle is 3 cm less than twice the width of the rectangle. If the perimeter is 75 cm, what are the dimensions of the rectangle?
If the length of a rectangle is 3 cm less than twice the width of the rectangle and the perimeter is 75 cm, then the length is 24 cm and width is 13.5 cm
Consider the width of the rectangle as w
The length of a rectangle is 3 cm less than twice the width of the rectangle
The length of the rectangle = 2w-3
Perimeter of the rectangle = 75 cm
Perimeter of the rectangle =2(l+w)
Where l is the length and w is the width of the rectangle
Substitute the values in the equation
2(2w-3+w) = 75
2(3w-3) = 75
6w-6 = 75
6w = 81
w = 13.5 cm
The length of the rectangle = 2(13.5)-3
=24 cm
Hence, If the length of a rectangle is 3 cm less than twice the width of the rectangle and the perimeter is 75 cm, then the length is 24 cm and width is 13.5 cm
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In a recent year, there were 29,757 traffic fatalities in the United States. Of these, 9001 were alcohol related.
(a) What is the probability that a bandomly selected traffic fatality in this year was alcohol related?
(b) What is the probability that a randomly selected traffic fatality in this year was not alcohol related?
(c) What is the probability that two randomly selected traffic fatalities in this year were both alcohol related?
(d) What is the probability that neither of two randomly selected traffic fatalities in this year were alcohol related?
(e) What is the probability that of two randomly selected traffic fatalities in this year, at least one was alcohol related?
we have found out the probability for different cases when there were 29,757 traffic fatalities in the United States and of these, 9001 were alcohol related.
Total traffic fatalities = 29,757
Alcohol related = 9001
(a) probability that a randomly selected traffic fatality in this year was alcohol related:
P = 9001 / 29,757 = 0.302
(b) probability that a randomly selected traffic fatality in this year was not alcohol related:
P = 1 - 0.302 = 0.698
(c) probability that two randomly selected traffic fatalities in this year were both alcohol related:
P = 0.302 × (9000 / 29756)
P = 0.091
(d)What is the probability that neither of two randomly selected traffic fatalities in this year were alcohol related:
P = 1 - 0.091
P = 0.909
(e) probability that of two randomly selected traffic fatalities in this year, at least one was alcohol related
P = 0.302 + 0.302 = 0.604
Therefore, we have found out the probability for different cases when there were 29,757 traffic fatalities in the United States and of these, 9001 were alcohol related.
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