Answer:
B
Step-by-step explanation:
area of top on triangle=1/2×4×3=6m²
area of four top triangles=6×4=24 m²
area of bottom square=4×4=16 m²
area of four side rectangles=4×(4×5)=80 m²
Total area= 24+16+80=120m²
A rectangular park is 8 miles long and 6 miles wide. How long is a pedestrian route that runs diagonally across the park?
Hey there! :)
Answer:
10 miles.
Step-by-step explanation:
To solve for the diagonal side, we can simply visualize the sides of the rectangle as sides of a right triangle with the diagonal being the hypotenuse.
We can use the Pythagorean Theorem (a² + b² = c²), where:
a = length of short leg
b = length of long leg
c = length of the diagonal
Solve:
c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = 10 miles. This is the length of the pedestrian route.
Answer:
10 milesSolution,
Hypotenuse (h) = R
Perpendicular (p) = 8 miles
Base (b) = 6 miles
Now,
Using Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
Plugging the values:
[tex] {r}^{2} = {(8)}^{2} + {(6)}^{2} [/tex]
Calculate:
[tex] {r}^{2} = 64 + 36[/tex]
[tex] {r}^{2} = 100[/tex]
[tex]r = \sqrt{100} [/tex]
[tex]r = 10 \: miles[/tex]
Length of route = 10 miles
Hope this helps...
Good luck on your assignment...
Which of the following equation is equivalent toY=2x+3? A. Y - 3 = 2(x-1) B. Y - 2x=3 C. Y - 3 = 2(x+1) D. Y + 2x = 3
Answer:
the answer is b
Step-by-step explanation:
Please help with this
Answer:
C) 42
Step-by-step explanation:
The parallel lines divide the transversals proportionally.
x/35 = 30/25
x = 35(6/5) . . . . multiply by 35, reduce the fraction
x = 42
An interior angle of a regular polygon has a measure of 108°. What type of polygon is it?
Answer:
Polygon is pentagon
Step-by-step explanation:
In a regular polygon each angle is equal.
In a regular polygon Each angle of polygon is given by (2n-4)90/n
where n is the number of sides of the polygon
given
An interior angle of a regular polygon has a measure of 108°.
(2n-4)90/n = 108
=> 180n - 360 = 108n
=> 180n-108n= 360
=> 72n = 360
=> n = 360/72 = 5
Thus, polygon has 5 sides
and we know that regular polygon which has 5 sides is called pentagon.
Thus, Polygon is pentagon
1. Growth of Functions (11 points) (1) (4 points) Determine whether each of these functions is O(x 2 ). Proof is not required but it may be good to try to justify it (a) 100x + 1000 (b) 100x 2 + 1000
Answer:
See explanation
Step-by-step explanation:
To determine whether each of these functions is [tex]O(x^2)[/tex], we apply these theorems:
A polynomial is always O(the term containing the highest power of n)Any O(x) function is always [tex]O(x^2)[/tex].(a)Given the function: f(x)=100x+1000
The highest power of n is 1.
Therefore f(x) is O(x).
Since any O(x) function is always [tex]O(x^2)[/tex], 100x+1000 is [tex]O(x^2)[/tex].
[tex](b) f(x)=100x^ 2 + 1000[/tex]
The highest power of n is 2.
Therefore the function is [tex]O(x^2)[/tex].
Answer:
i think its 2000
Step-by-step explanation:
Assume that the year has 366 days and all birthdays are equally likely. Find the probability that two people chosen at random were born on the same day of the week.
Answer:
[tex]\dfrac{1}{7}[/tex]
Step-by-step explanation:
There are 7 days in a week.
For the first person, we select one day out of the 7 days. The first person has 7 options out of the 7 days.
Let Event A be the event that the first person was born on a day of the week.
Therefore:
[tex]P(A)=\dfrac{7}{7}=1[/tex]
The second person has to be born on the same day as the first person. Therefore, the second person has 1 out of 7 days to choose from.
Let Event B be the event that the second person was born.
Therefore, the probability that the second person was born on the same day as the first person:
[tex]P(B|A)=\dfrac{1}{7}[/tex]
By the definition of Conditional Probability
[tex]P(B|A)=\dfrac{P(B \cap A)}{P(A)} \\$Therefore:\\P(B \cap A)=P(B|A)P(A)[/tex]
The probability that both were born on the same day is:
[tex]P(B \cap A)=P(B|A)P(A) = \dfrac{1}{7} X 1 \\\\= \dfrac{1}{7}[/tex]
Find the equation of a line passing through the point (-4,1) and perpendicular to the
line 3y = 12x - 9.
Answer:
A. y=-1/4x
Step-by-step explanation:
We have the information 3y=12x-9, the lines are perpendicular, and the new line passes through (-4,1). First, you want to put the original equation into slope intercept form by isolating the y, to do this we need to divide everything by 3 to get y=4x-3. The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 4, so flip it to 1/4 and multiply by -1, we get the slope of the new line as -1/4. So far we have the equation y=-1/4x+b. We are given a point on the line, (-4,1), we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as 1=-1/4(-4)+b. First you multiply to get 1=1+b, then you subtract 1 from both sides to isolate the variable and you get b=0. Then you can use b to complete your equation with y=-1/4x, or letter A.
The product of an irrational number and a rational number is irrational. Sometimes True Always True Never True
Answer:
Always true
Step-by-step explanation:
If you can't express the number as a ratio of integers, multiplying or dividing it by integers will not make it so you can.
If π is irrational, 2π is also irrational.
It is always true that the product of a rational and an irrational number is irrational.
Answer:
all ways true
Step-by-step explanation:
answer if u love cats & dogs
Answer:
(7, 5.25) lies on the graph.
Step-by-step explanation:
We are given the following values
x = 4, 6, 8, 12 and corresponding y values are:
y = 3, 4.5, 6, 9
Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.
Equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:
[tex]y=mx+c[/tex]
where m is the slope.
(x,y) are the coordinates from where the line passes.
c is the y intercept.
Here,
[tex]x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5[/tex]
Formula for slope is:
[tex]m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}[/tex]
Now, the equation of line becomes:
[tex]y=\dfrac{3}{4}x+c[/tex]
Putting the point (4,3) in the above equation to find c:
[tex]3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0[/tex]
So, final equation of given function is:
[tex]y=\dfrac{3}{4}x[/tex]
OR
[tex]4y=3x[/tex]
As per the given options, the point (7, 5.25) satisfies the equation.
So correct answer is [tex](7, 5.25)[/tex].
A half marathon is 13.1 miles long. Leah is running a half marathon and has completed 7.75 miles. How many miles to
the finish line?
Answer:
5.35 more miles
Answer:
5.35 miles to the finish line
Step-by-step explanation:
Step one
13.1-7.75=
5.35
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n. Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle) Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles) Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p Step 4: So, m∠m + m∠n = m∠p In which step did the student first make a mistake and how can it be corrected? Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles) Step 2; m∠p − m∠o = 90 degrees (alternate interior angles)
Answer:
(A)Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)
Step-by-step explanation:
In the triangle, the exterior angle = pThe adjacent interior angle =oThe two opposite angles are marked m and nThe steps followed by the student are:
Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
We observe that the student made a mistake in Step 1, it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle).
p is outside the triangle, therefore it cannot form one of the angles in the triangle.
A survey of 61,647 people included several questions about office relationships. Of the respondents, 26% reported that bosses scream at employees. Use a 0.05 significance level to test the claim that more than ¼ of people say that bosses scream at employees.
Step-by-step explanation:
n = 61,647, p = 0.26, q = 0.74
μ = p = 0.26
σ = √(pq/n) = 0.00177
At 0.05 significance, z = 1.96.
0.26 ± 1.96 × 0.00177
(0.257, 0.263)
0.25 is outside of the confidence interval, so we can conclude with 95% confidence that the proportion is greater than 0.25.
CAN SOMEONEHELP PLS ASAP
Answer:
a ≈ 2.2
Step-by-step explanation:
Using the Cosine rule in Δ ABC
a² = b² + c² - 2bc cos A
Here b = 3, c = 4 and A = 32° , thus
a² = 3² + 4² - (2 × 3 × 4 × cos32° )
= 9 + 16 - 24cos32°
= 25 - 24cos32° ( take the square root of both sides )
a = [tex]\sqrt{25-24cos32}[/tex] ≈ 2.2
Good Morning can I get some help please?
Answer:
5x + 10 = 25
Subtract 10 on each side to make x alone
5x = 15
divide by 5 on each side
x=3 so x=3
3x + 12 = 48
48-12=36
3x=36
divide by 3
x=12
4x + 8 = 16
4x = 8
x=2
2x + 15=25
2x=10
x=5
5x + 20 = 50
5x=30
x=6
hope this helps
1. 3
2.12
3.2
4.5
5.6
Step-by-step explanation:
Answer:
x = 3x = 12x = 2x = 5x = 6Step by step explanation
First:
Move the constant to the Right Hand Side and change its signCalculate the differenceDivideCalculateSolution,
1. 5x + 10 = 25
Move constant to the R.H.S and change its sign:
5x = 25 - 10
Calculate the difference
5x = 15
Divide both sides by 5
5x/5 = 15/5
calculate
X = 3
2. 3x + 12 = 48
or, 3x = 48 - 12
or, 3x = 36
or, 3x/x = 36/3
x = 12
3. 4x + 8 = 16
or, 4x = 16 - 8
or, 4x = 8
or, 4x/x = 8/4
x = 2
4. 2x + 15 = 25
or, 2x = 25 - 15
or, 2x = 10
or, 2x/x= 10/2
x = 5
5. 5x + 20 = 50
or, 5x = 50-20
or, 5x = 30
or, 5x/x = 30/5
x = 6
Hope this helps...
Good luck on your assignment...
the quotient of F and the product of r,s, and T
Behold the quotient of F and the product of r,s, and T: F / (r·s·T)
The numerical of the statement the quotient of F and the product of r,s, and T is F/(r×s×T).
What are quotient, remainder, divisor, and dividend?The number which is being divided is the dividend.
The number with which we are dividing is the divisor.
The result when a dividend is divided by the divisor is the quotient.
A remainder is the extra portion of a number when it isn't completely divisible.
Given, Are some variables F, r, s, and t.
Now, The product of r,s, and T is,
= r×s×T and the complete statement the quotient of F and the product of r,s, and T can be written as,
F/(r×s×T).
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Write an expression that is divisible by 7. Use it to find two three-digit numbers numbers divisible by 7.
Answer:
7x+7 is obviously divisible by 7.
put in any value high enough and you can find the two three digit numbers.
Step-by-step explanation:
Two three-digit numbers divisible by 7 are 98 and 105.
Two three-digit numbers divisible by 7 are 98 and 105.To create an expression that is divisible by 7, we can use the property that the difference between two numbers is divisible by 7 if the numbers themselves are divisible by 7.
Let's represent a three-digit number divisible by 7 as "7k" where k is an integer. To find two three-digit numbers divisible by 7, we can use the following expression:
7k - 7
For example, if we substitute k = 15, we get:
7(15) - 7 = 105 - 7 = 98
So, the first three-digit number divisible by 7 is 98.
Similarly, for the second three-digit number, let's substitute k = 16:
7(16) - 7 = 112 - 7 = 105
Therefore, the two three-digit numbers divisible by 7 are 98 and 105.
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At a DBE lecture of 100 students, there are 29 women and 23 men. Out of these students, 4 are teachers and 24 are either men nor teachers. Find the number of women teachers attending the lecture
Answer:
20 teachers
Step-by-step explanation:
Because if you take 100 and minus it by 29, 23, 4 and 24 you get 20.
The Nutty Professor sells cashes for $6.00 per pound and Brazil nuts for $5.30 per pound. How much of
each type should be used to make a 35 pound mixture that sells for $5.64 per pound?
Answer:
17 pound of cashew and 18 pound of Brazil nutsStep-by-step explanation:
Let X be the amount of cashews that the nutty professor will mix.
Since, the total weight of the nuts should be 35 lbs
The amount of Brazil nuts = 35 - X
Now,
[tex]6x + 5.30(35 - x) = 5.64(35)[/tex]
[tex]600x + 530(35 - x) = 564 \times 35[/tex]
[tex]600x + 18550 - 530x = 19740[/tex]
[tex]70x = 19740 - 18550[/tex]
[tex]70x = 1190[/tex]
[tex]x = \frac{1190}{70} [/tex]
[tex]x = 17[/tex]
Again,
[tex] 35 - x[/tex]
[tex]35 - 17[/tex]
[tex]18[/tex]
17 pounds of cashew and 18 pounds of Brazil nuts.
Hope this helps...
Good luck on your assignment...
g a) What are some of the distinguishing properties of a normal Distribution? Discuss b) The sampling distribution of the sample means is the curve that describes how the sample means are distributed. True or False Explain c) The mean of sample means is the same as the population for a given sample of size n. True False Explain
Answer:
a) Check Explanation.
b) True. Check Explanation.
c) True. Check Explanation.
Step-by-step explanation:
a) A normal distribution is one which is characterized by four major properties.
- A normal distribution is symmetrical about the center of the distribution. That is, the variables spread out from the center in both directions in the same manner; the right side of the distribution is a mirror image of the left side of the distribution.
The center of a normal distribution is located at its peak, and 50% of the data lies above the mean, while 50% lies below.
- The mean, median and the mode are coincidental. The mean, median and mode of a normal distribution are all the same value.
- A normal distribution is unimodal, that is, has only one mode.
- The ends of the probability curve of a normal distribution never touch the x-axis, hence, it is said too be asymptotic.
b) The sampling distribution of sample means arises when random samples are drawn from the population distribution and their respective means are computed and put together to form a distribution. Hence, the curve of this sampling distribition of sample means will show how the sample means are distributed. Hence, this statement is true.
c) The Central Limit Theorem gives that if the samples are drawn randomly from a normal distribution and each sample size is considerable enough, the mean of the sampling distribution of sample means is approximately equal to the population mean. So, if the conditions stated are satisfied, then thos statement too, is true.
Hope this Helps!!!
Let S be a sample space and E and F be events associated with S. Suppose that Pr (Upper E )equals 0.6, Pr (Upper F )equals 0.2 and Pr (Upper E intersect Upper F )equals 0.1. Calculate the following probabilities. (a) Pr (E|F )(b) Pr (F|E )(c) Pr (E| Upper F prime )(d) Pr (Upper E prime | Upper F prime )
Answer:
(a)0.5
(b)0.17
(c)0.625
(b)0.375
Step-by-step explanation:
Pr(E)=0.6
Pr(F)=0.2
[tex]Pr(E\cap F)=0.1.[/tex]
(a)Pr (E|F )
[tex]Pr (E|F )=\dfrac{Pr(E \cap F)}{Pr(F)} \\=\dfrac{0.1}{0.2}\\\\=0.5[/tex]
(b)Pr (F|E )
[tex]Pr (F|E )=\dfrac{Pr(E \cap F)}{Pr(E)} \\=\dfrac{0.1}{0.6}\\\\=0.17[/tex]
(c)Pr (E|F')
Pr(F')=1-P(F)
=1-0.2=0.8
[tex]Pr(E \cap F')=P(E)-P(E\cap F)\\=0.6-0.1\\=0.5[/tex]
Therefore:
[tex]Pr (E|F' )=\dfrac{Pr(E \cap F')}{Pr(F')} \\=\dfrac{0.5}{0.8}\\\\=0.625[/tex]
(d)Pr(E'|F')
[tex]P(E'\cap F')=P(E \cup F)'\\=1-P(E \cup F)\\=1-[P(E)+P(F)-P(E\cap F)]\\=1-[0.6+0.2-0.1]\\=1-0.7\\=0.3[/tex]
Therefore:
[tex]Pr (E'|F' )=\dfrac{Pr(E' \cap F')}{Pr(F')} \\=\dfrac{0.3}{0.8}\\\\=0.375[/tex]
Want Brainliest? Get this correct Which of the following is the quotient of the rational expressions shown below?
Answer:
[tex]\dfrac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
Invert the denominator and multiply.
[tex]\dfrac{2x+5}{3x}\div\dfrac{2x-1}{2x+1}=\dfrac{2x+5}{3x}\cdot\dfrac{2x+1}{2x-1}\\\\=\dfrac{(2x+5)(2x+1)}{(3x)(2x-1)}=\boxed{\dfrac{4x^2+12x+5}{6x^2-3x}}\qquad\text{matches choice A}[/tex]
Answer:
[tex]\frac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
After using the reciprocal of the second term, the denominator will multiply out to be [tex]6x^2-3x[/tex]. There is only one option with that as the denominator so it must be the correct answer.
Two cities whose longitudes are 10E and 20W on the equator are apart
Step-by-step explanation:
to be honest I'm not sure how to do
If x = 2, then 2x = 4
Answer:
4 = 4
Step-by-step explanation:
=> 2x = 4
Putting x = 2
=> 2(2) = 4
=> 4 = 4
Answer:
TrueSolution,
X= 2
Now,
2x=4
plugging the value of X,
2*2= 4
4 = 4 ( hence it is true)
Rachel measured the lengths of a random sample of 100 screws. The mean length was 2.9 inches, and the population standard deviation is 0.1 inch. To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?
Answer:
z = 10
Step-by-step explanation:
The value of the z-statistic is given by:
[tex]z = \frac{X - \mu}{s}[/tex]
In which:
X is the measured value.
[tex]\mu[/tex] is the expected value.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex] is the standard deviation of the sample. [tex]\sigma[/tex] is the standard deviation of the population.
In this question:
The mean length was 2.9 inches, and the population standard deviation is 0.1 inch.
This means that [tex]\mu = 2.9, \sigma = 0.1[/tex]
Random sample of 100 screws.
This means that n = 100.
To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?
3 inches, so [tex]X = 3[/tex]
[tex]s = \frac{0.1}{\sqrt{100}} = 0.01[/tex]
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{3 - 2.9}{0.01}[/tex]
[tex]z = 10[/tex]
Answer:
-10
Step-by-step explanation:
If we first note the denominator of fraction numerator sigma over denominator square root of n end fraction equals fraction numerator 0.1 over denominator square root of 100 end fraction equals fraction numerator begin display style 0.1 end style over denominator 10 end fraction equals 0.01
Then, getting the z-score we can note it is z equals fraction numerator x with bar on top minus mu over denominator begin display style 0.01 end style end fraction equals fraction numerator 2.9 minus 3 over denominator 0.01 end fraction equals negative 10
This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away.
The function f(x) = x^2+4 is defined over the interval (-2,2). If the interval is dived into n equal parts what is the height of the right endpoint of the kth rectangle?
Answer:
Option (A).
Step-by-step explanation:
The function f(x) = x² + 4 is defined over the interval (-2, 2)
Total number of equal parts between this interval = 5
If the interval is divided into n equal parts, height of the right endpoint of each rectangle = [tex]\frac{5}{n}[/tex]
Height of the endpoint of the k rectangles = [tex]k.\frac{5}{n}[/tex]
Therefore, height of the endpoint of the kth rectangle = Height of first rectangle + height of k rectangles
= -2 + [tex]k.\frac{5}{n}[/tex]
Option (A). will be the answer.
The height of the right endpoint of the kth rectangle h = -2 + k (5/n)
What is the height?The height is a vertical distance between two points. In the case of the triangle, the height will be the distance between the base and the top vertex of the triangle.
The function f(x) = x² + 4 is defined over the interval) (-2, 2 )
Total number of equal parts between this interval = 5
If the interval is divided into n equal parts, the height of the right endpoint of each rectangle = (5/n)
Height of the endpoint of the k rectangles = k (5/n)
The height of the endpoint of the kth rectangle:-
= Height of first rectangle + height of k rectangles
= -2 + k ( 5/n )
Therefore the height of the right endpoint of the kth rectangle h = -2 + k (5/n)
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What is the solution to the system of linear equations below?
x+4y=22
2x+y=9
Answer:
[tex]\boxed{\sf \ \ \ x = 2 \ \ and \ \ y = 5 \ \ \ }[/tex]
Step-by-step explanation:
hello, we have two equation
(1) x + 4y = 22
(2) 2x + y = 9
let's multiply (1) by 2 and subtract (2)
2x + 8y - (2x + y) = 2*22 - 9 = 44 - 9 = 35
<=> 2x + 8y -2x -y = 35
<=> 7y = 35
<=> y = 35/7 = 5
we replace this value in (1) and it comes
x + 4*5 = 22
<=> x = 22 - 20 = 2
so the solution is
x = 2 and y = 5
hope this helps
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Three hundred feet of fencing is used
dimensions of the playground that maximize the total enclosed area. What is the maximum area?
The smaller dimension is
feet
Answer:
50 ft by 75 ft3750 square feetStep-by-step explanation:
Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...
y = (300 -2x)/3
And the enclosed area is ...
A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)
This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.
The maximum area is enclosed when the dimensions are ...
50 ft by 75 ft
That maximum area is 3750 square feet.
_____
Comment on the solution
The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).
You spend 6,380.00 a year for rent. This is 22% of your income. What is your income?
Answer: 29,000.00
Step-by-step explanation:
Let the income=x. 22%=0.22.
So 6380/x=0.22
x=6380/0.22=29,000.00
Legal descriptions tend to prefer neat straight lines from point to point, regardless of describing a square, rectangle, triangle or even a smooth circle. When might a property boundary end up being a squiggly line?
Answer:
When describing a property line drawn down the center of a creek bed
A person has a bag containing dimes and nickels. There are a total of 120 coins in the bag, and the total value of the coins is $9.25. Determine how many dimes and nickels are in the bag. There are _____dimes. There are _____ nickels.
Answer:
There are 65 dimes. There are 55 nickels.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of dimes
y is the number of nickels.
There are a total of 120 coins in the bag
This means that x + y = 120.
The total value of the coins is $9.25.
The dime is worth $0.10 and the nickel is worth $0.05. So
0.1x + 0.05y = 9.25
System:
[tex]x + y = 120[/tex]
[tex]0.1x + 0.05y = 9.25[/tex]
From the first equation:
[tex]y = 120 - x[/tex]
Replacing in the second:
[tex]0.1x + 0.05y = 9.25[/tex]
[tex]0.1x + 0.05(120 - x) = 9.25[/tex]
[tex]0.1x + 6 - 0.05x = 9.25[/tex]
[tex]0.05x = 3.25[/tex]
[tex]x = \frac{3.25}{0.05}[/tex]
[tex]x = 65[/tex]
[tex]y = 120 - x = 120 - 65 = 55[/tex]
There are 65 dimes. There are 55 nickels.