5. The corresponding sides of the similar shapes have same
- In the figure given below, what is the value of x? (RED)
2 cm
3 cm
3 cm
2 cm
4 cm
x cm
(GR
4 cm
Answers
Using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.
What exactly are mathematical operations?An operation, in mathematics, is a mathematical function that transforms zero or more input values into a precisely defined output value.
The arity of the operation is influenced by the number of operands.
PEMDAS, parenthesis, exponents, multiplication, and division.
So, the value of x will be:
The given two rectangles have similar sides.
2cm is similar to 4cm.
3cm is similar to xcm.
Now, we can calculate x as follows:
2/4 = 3/x
2x = 4×3
2x = 12
x = 12/x
x = 6
Therefore, using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.
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Related Questions
An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed from these oranges is approximately normally distributed, with a mean of 4.10 ounces and a standard deviation of 0.20 ounce. Suppose that you select a sample of 16 oranges.
a. What is the probability that the sample mean amount of juice will be at least 4.03ounces?
b. The probability is 74% that the sample mean amount of juice will be contained between what two values symmetrically distributed around the population mean?
c. The probability is 78% that the sample mean amount of juice will be greater than what value?
Answers
The measures, using the normal distribution and the central limit theorem, are given as follows:
a) Probability of at least 4.03 ounces: 0.9192 = 91.92%.
b) Probability of 74% that it is between 4.04 ounces and 4.16 ounces.
c) Probability of 78% that it is greater than 4.06 ounces.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The parameters regarding the amount of juice squeezed from these oranges are given as follows:
[tex]\mu = 4.10, \sigma = 0.2, n = 16, s = \frac{0.2}{\sqrt{16}} = 0.05/tex]
The probability that the sample mean amount of juice will be at least 4.03 ounces is one subtracted by the p-value of Z when X = 4.03, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (4.03 - 4.10)/0.05
Z = -1.4.
Z = -1.4 has a p-value of 0.0808.
1 - 0.0808 = 0.9192.
Considering the symmetry of the normal distribution, the middle 74% of the measures is bounded by:
The 13th percentile, which is X when Z = -1.125.The 87th percentile, which is X when Z = 1.125.Hence the lower bound is:
[tex]Z = \frac{X - \mu}{s}[/tex]
-1.125 = (X - 4.10)/0.05
X - 4.10 = -1.125 x 0.05
X = 4.04.
The upper bound is:
[tex]Z = \frac{X - \mu}{s}[/tex]
1.125 = (X - 4.10)/0.05
X - 4.10 = 1.125 x 0.05
X = 4.16.
The probability is 78% that the sample mean amount of juice will be greater than the 22th percentile, which is X when Z = -0.77, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
-0.77 = (X - 4.10)/0.05
X - 4.10 = -0.77 x 0.05
X = 4.06 ounces.
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An exercise machine with an original price of $890 is on sale at 24% off.
a. What is the discount amount?
b. What is the exercise machines sale price?
Answers
The discount amount is $213.6
The sale price for the exercise machines is $676.4
How to calculate the discount amount ?The first step is to calculate the discount amount
890 × 24/100
= 890 × 0.24
= 213.6
The next step is to calculate the sale price
890(1-0.24)
890(0.76)
676.4
Hence the discount amount is $213.6 and the sale price of the exercise machine is $676.4
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When choosing the linear equation that represents the graph, I can look at the direction of the line and automatically know if the slope is a positive or negative number
Question 1 options:
True
False
Answers
True. You can look at the direction of the line and automatically know if the slope is a positive or negative number.
The linear equation with positive value of slope goes upwards from left to right and linear equation with negative value of slope goes downwards from left to right.
Thus, it is true that you can look at the direction of the line and automatically know if the slope is a positive or negative number.
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Harper's car used 9 gallons to travel 171 miles. How many miles can the car go for each gallon of gas?
Answers
Answer:
Step-by-step explanation:
7
Determine which vehicle to purchase based on monthly payment.
A. Final sale price $25,000, 5
% interest, and offer financing for 60 months
B. Final sale price $29,000, 4% interest and offers financing for 72 months.
Answers
The amount paid to vehicle A is less than to vehicle B so, Vehicle A is suitable to purchase based on a monthly payment.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
For vehicle A,
The Principal amount of the car, P = $25000,
The rate of interest, r = 5% = 5/100 = 0.05,
The tenure, n = 60 months = 60/12 = 5 years,
Calculate the amount by the formula given below,
A = P (1 + r)ⁿ
Here A is the amount,
Substitute the values,
A = 25000 (1 + 0.05)⁵,
A = $31907.03
Similarly, for vehicle b
A = 29000 (1 +0.04)⁶
A = $36694.25
As the amount of vehicle A is less than the of vehicle B Therefore, vehicle A is suitable to buy.
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b) When the cost of the ingredients rises, the tuckshop increases its prices. A cherry muffin now costs 350 shillings. A blueberry muffin now costs the same as three damson ones. A apple and a blueberry muffin now cost as much as a cherry muffin. A cherry muffin and two damson ones now cost the same as two apple and one blueberry. How much would Aanya now spend to buy one of each?
Answers
Aanya will now buy each at the cost below
A cherry muffin costs 350 shillings
A blueberry muffin costs 210 shillings
An apple costs 140 shillings
damson ones costs 70 shillings
How to determine the cost of eachThe information given in the question is interpreted as below
A cherry muffin = 350 shillings
A blueberry muffin = 3 * damson ones
An apple + a blueberry muffin = 1 cherry muffin
A cherry muffin + 2 damson ones = 2 apple + 1 blueberry
from: 1 blueberry muffin, B = 3 * damson ones, D
D = B / 3
Also, An apple, A + B = 1 cherry muffin, C
A = C - B
C + 2D = 2A + B
substituting the values
350 + 2 * (B/3) = 2 * (350 - B) + B
350 + 2B/3 = 700 - 2B + B
collecting like terms
2B/3 + B = 700 - 350
5B/3 = 350
5B = 1050
B = 1050/5
B = 210
Solving for cost of apple
A = C - B = 350 - 210 = 140
Solving for the cost of the damson ones
D = B / 3 = 210 / 3 = 70
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The polynomial function f(x) is graphed below. Fill in the form below regarding the features of this graph.
Answers
Answer:
Even and Positive
Step-by-step explanation:
The photography club is selling hot chocolate at soccer games to raise money for new cameras. The table shows their profit per game for the first five games.
the graph is below
Game Profit ($)
1 −12.50
2 −10.15
3 18.65
4 25.90
5 45.75
Based on the average profit per game, how much total money can the club expect to earn by the end of the 10-game season?
__ dollar(s)
Answers
Based on the average profit per game, the total money which this club should expect to earn by the end of the 10-game season is $80.21.
How to find a trend line for the data?In order to determine a linear equation of the trend line (line of best fit) that models the data points contained in the table, we would have to use a scatter plot.
In this scenario, the number of games would be plotted on the x-axis of the scatter plot while the profit (in dollars) would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the trend line on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the data points in the table, a linear equation of the trend line is given by:
y = 8.23x - 2.09
By the end of the 10-game season, the average profit per game is given by:
y = 8.23x - 2.09
y = 8.23(10) - 2.09
y = 82.3 - 2.09
y = $80.21.
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Select all of the following that are quadratic functions. x = 3y2 – 6y + 5 y + 3 = –2 x 2+ 5 y = 2 x 2 – 8 x + 6 y= –7 x – 4 y – 3 x = 4 x 3 – x2 + 9 y = 5 x(x + 9) – 8 y – 2 x 2 = 3 x – 2 x 2 + 4
Answers
The quadratic functions in this problem are listed as follows:
x = 3y2 – 6y + 5.y + 3 = -2x² + 5.y = 2x² - 8x + 6.y = 5x(x + 9) - 8.What is the definition of a quadratic function?The definition of a quadratic function is presented as follows:
y = ax² + bx + c.
In which the leading coefficient a has to assume a value different of zero.
Another format to represent a quadratic function is making the input variable y and the output variable x, which is an exchange of the conventional notation, hence:
x = ay² + by + c.
The non-quadratic functions in this problem are:
y = -7x - 4 -> Linear function, as the highest exponent is of one.y - 3x = 4x³ - x² + 9. -> Cubic function, as the highest exponent of three.All the other functions are quadratic functions, as they have two as the highest exponent, with a leading coefficient different of zero.
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Find the chi-square value x2l corresponding to a sample size of 4 and a confidence level of 98 percent.
Answers
The critical values for the chi-square distribution, with a sample size of 4 and a confidence level of 98 percent, are of:
0.2971 and 13.2767.
How to obtain the critical value for the chi-square distribution?The critical value for the chi-square distribution is obtained inserting these following information into a calculator:
The tail of the test, whether it is left tailed, right tailed or two tailed.The number of degrees of freedom, which is one less than the sample size.The significance level, which is one subtracted by the decimal equivalent of the confidence level.In the context of this problem, with a sample size of 4 and a confidence level of 98 percent, the parameters are given as follows:
Two-tailed test, as it is standard since it says nothing about the tail.3 degrees of freedom, which is one less than the sample size of 4.Significance level of 0.02, as the subtraction of one by the confidence level of 0.98 is of 0.02.Inserting these information into the calculator, the critical values are given as follows:
0.2971 and 13.2767.
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Your utility company charges 13 cents per kilowatt-hour of electricity. Complete parts (a) and (b) below.
a. What is the daily cost of keeping lit a 60-watt light bulb for 10 hours each day?
b. How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light
using only 15 watts of power?
a. The daily cost of keeping lit a 60-watt light bulb for 10 hours each day is $
(Round to three decimal places as needed.)
b. The yearly savings of replacing the 60-watt light bulb with a 15-watt light bulb is $
(Round to two decimal places as needed.)
Answers
Answer: a) $78 per day
b) $21,352.50
Step-by-step explanation:
a) 60x10=600
600x0.13= $78 per day
b) 15x10=150
150x0.13=$19.50 per day
19.50x365= $7,117.50 per year (with a 15watts lightbulb)
$78x365=$28,470 per year (with a 60watts lightbulb)
$28,470-7,117.50= $21,352.50
Which number sentence is true?
A.
B.
C.
D.
Answers
The number sentence 4.8 < √32 is true
How to determine which number sentence is true?A number sentence is an arrangement of numbers and mathematical operation symbols
Given:
For 3 1/3 < √7
3 1/3 = 3.33 and √7 = 2.65
3.33 < 2.65
This is not true
For 4.8 < √32
√32 = 5.66
4.8 < 5.66
This is true
For |-3.2| < |-3.1|
|-3.2| = 3.2 Note: when you see sign | | you neglect the sign
|-3.1| = 3.1
3.2 < 3.1
This is not true
For 5.3×10⁵ < 9.76× 10⁴
5.3×10⁵ = 5.3×100000 = 530000
9.76× 10⁴ = 9.76×10000 = 97600
530000 < 97600
This is not true
Therefore, the number sentence 4.8 < √32 (4.8 < 5.66) is true. So option B is the answer
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(15x + 3)
108
Solve for x
Answers
Answer:
(15x+3)° = 108 (vertically opposite angles)
15x = 108-3
15x = 105
x = 105/15
x =7
y = -x + 10| what is the axis of summetry
Answers
The axis of symmetry of function y = -|x + 10| is at y = 0
Axis of symmetry is an imaginary straight line which divide the function into two equal parts.
Axis of symmetry creates a mirror image of other part.
If we fold the two parts then the parts will superimposed.
Given function,
y = -|x + 10|
is in form y = a |x - h| + k
here , (h, k) is vertex
Comparing the form to the given equation
(h, k) = (-10 , 0)
which means graph is opens upward
and a = -1
Hence, the equation of axis of symmetric is at y = 0
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The Magazine Mass Marketing Company has received 16 entries in its latest sweepstakes. They know that the probability of receiving a magazine subscription order with an entry form is 0.4. What is the probability that no more than 3 of the entry forms will include an order? Round your answer to four decimal places.
Answers
Answer: The probability that more than 12 of the entry forms will include an order is 0.624.
What is probability?
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
The Magazine Mass Marketing Company has received 16 entries in its latest sweepstakes.
The probability that more than 12 of the entry forms will include an order can be found as:
P(X > 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P( X = 3) - P(X = 4)
P(X > 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4)
P(X > 4) = 1 - 0.0009 - 0.0097 - 0.043 - 0.117 - 0.205
P(X > 4) = 0.624
Thus, the probability that more than 12 of the entry forms will include order is 0.624.
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Step-by-step explanation:
When buying stock, there are often fees with the purchase. If a broker is charging a flat percentage of 2% for a trade, and you trade 1,000 shares at $5 each, what is the total amount charged by the broker?
Answers
The broker charged $100.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total shares = 1000
Price for each shares= $5.
So, the total price of 1000 shares= $5000
If broker is charging a flat percentage of 2% for a trade.
Then, the broker charged for 1000 trade
= 5000 x 0.02
= $100.
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Need help with this
Answers
Step-by-step explanation:
please recheck your question..
There is no question attached.
hope it helps..
Lisa collected leaves from different trees for a science project. Every day for a week (7 days), she collected 7 leaves. How many leaves did she collect by the end of the week?
Answers
an arts academy requires there to be 5 teachers for every 115 students and 6 tutors for every 54 students. how many students the academy have per teacher? per tutor? how many tutors does the academy need if it has 72 students
Answers
The number of students per teacher is 23.
The number of students per tutor is 8.
The number of tutors needed for 72 students is 9.
What is the number of students per teacher and per tutor?In order to determine the number of students per teacher, divide the total number of teachers by the total number of students.
Students per teacher = total number of students / total number of teachers
115 /5 = 23 students per teacher
In order to determine the number of students per tutor, divide the total number of tutors by the total number of students.
Students per tutor = total number of students / total number of tutors
54 / 6 = 9 students per tutor
The number of tutors needed for 72 students = total number of students / students per tutor
72 / 9 = 8 tutors
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Workbook Reference:
Perform the indicated operations. Write answer in descending order.Add -13x + 9 - 10y, 9x - 7y and -12x - 3y + 8
Answers
Answer:
−16x − 20y + 17
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
Find X and Y. Give reasons to justify your answer
Answers
Answer:
x = 8. y = 21
Step-by-step explanation:
x + 8x + 18 = 90
combine like terms
9x + 18 = 90
-18 both sides
9x = 72
divide by 9 both sides
x = 8
______
3y + 27 = 90
-27 both sides
3y = 63
divide by 3 both sides
y = 21
What is the reciprocal of 3 ⅞
Answers
Answer:
[tex]\frac{8}{31}[/tex]
Step-by-step explanation:
the reciprocal of a number n is [tex]\frac{1}{n}[/tex]
given
3 [tex]\frac{7}{8}[/tex] ← express as an improper fraction
= [tex]\frac{31}{8}[/tex] , then
reciprocal = [tex]\frac{1}{\frac{31}{8} }[/tex] = [tex]\frac{8}{31}[/tex]
Answer:
[tex]\displaystyle \frac{8}{31}[/tex]
Step-by-step explanation:
First, we will turn 3 ⅞ into an improper fraction.
[tex]\displaystyle (3*\frac{8}{8} )+(\frac{7}{8} )=\frac{24}{8} +\frac{7}{8} = \frac{31}{8}[/tex]
Next, we will find the reciprocal. This means we flip the numerator and the denominator.
[tex]\displaystyle \frac{31}{8} \rightarrow \frac{8}{31}[/tex]
The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
Answers
The equation that is used to find the length of the legs of the triangle is
0.5(x)(x + 2) = 24 , x² + (x + 2)² = 100 and x² + 2x – 48 = 0
The area of the triangle is 24 square feet.
We know that the area of a triangle is given by the formula
1/2 × base × height.
Now in the attached figure we can see that the length of the base is x feet
The height of the right-angled triangle is (x+2) feet.
So the area of the triangle will be:
area = 1/2 · (x) · (x+2)
or, area = 0.5x(x+2)
But the area of the triangle is 24 square feet. Therefore the Equation to find the legs will be 0.5x(x+2) = 24.
Now if we use the properties of Pythagoras theorem we can write the formula as
hypotenuse² = sum of squares of legs
10² = x² + (x+2)²
Therefore we get the second equation.
Now simplifying the above equation we get:
10² = x² + (x+2)²
or, 2x² + 4x - 96 = 0
or, x² + 2x - 48 = 0
This is the third option.
Therefore the required equation are:
0.5(x)(x + 2) = 24 , x² + (x + 2)² = 100 and x² + 2x – 48 = 0 .
Disclaimer: The missing image of the triangle is attached below.
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Which graph represents the function f(x) = −lx + 3|?
Answers
Is anyone able to solve this?
Answers
Explanation:
To find x we need to find the unknown side that connects the two triangles using the Pythagorean theorem:
a² + b² = c² (c is always hypotenuse)
So:
a² + 6² = 9²
a² = 9² - 6²
a² = 81 - 36
a² = 45
a = sqrt45
Now we do the same thing for the other triangle:
x² + 5² = sqrt45²
x² + 25 = 45
x² = 20
x = 2√5 or 4.5...
The price of an item has risen to $169 today. Yesterday it was $130. Find the percentage increase.
Answers
Answer:30%
Step-by-step explanation:
Step-by-step explanation:
so,
100% = $130
1 % = 100%/100 = 130/100 = $1.30
the price changed by 169 - 130 = $39.
how many % are that ?
as many % and times 1% fits into $39 :
39 / 1.3 = 30%
the price increase was 30%.
If C is to be chosen at random from the set 1,2,3, 4 And D is to be chosen at a random from the set 1234. What is the possiblity C, D would be Odd?
Answers
The probability that C and D would be odd according to the given task content is; 1/4.
What is the probability that C and D would be odd?It follows from the task content that the probability that C and D would be odd be determined.
Given that the C and D are each chosen from a set 1, 2, 3, 4.
The probability that C is odd would be;
P (C is odd) = 2/4 = 1/2
Also; P ( D is odd) = 1/2
Consequently, the probability that C and D would be odd is;
= 1 / 2 × 1 / 2
= 1 / 4.
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HELP!! Will give brainiest
Answers
Answer:
C ≈ 207.3 ft
Step-by-step explanation:
the circumference (C) of a circle is calculated as
C = 2πr ( where r is the radius ) , then
C = 2π × 33 = 66π ≈ 207.3 ft ( to the nearest tenth )
Answer:
103.67 feet
Step-by-step explanation:
using C = pi d
3 cups of cashews for 4 cups of flour how many cups of flour for 2 cups of cashews
Answers
The cups of flour required for 2 cups of cashew is 2.6667
How to find the proportion for 2 cups of cashewsThe proportion given in the problem is 3 cups of cashews for 4 cups of flour.
From the given proportion we calculate for the quantity of flours required for 2 cups of cashew
3 cups of cashew = 4 cups of flours
2 cups of cashew = ?
cross multiplying
3 * ? = 4 * 2
? = 4 * 2 / 3
? = 8 / 3
? = 2.6667
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I need help with this please help me
Answers
Answer:
y = 122
x = 58
Step-by-step explanation:
Parallel line angle rule, corresponding angle are equal
so y = 122
A flat line has 180degree angle
to get x, flat line - y = 180 - 122 = 58