Let's call the number of hours of labor required to replace the water pump as "x".
The total cost of the water pump and labor was $668, so we can write an equation:
$490 + $89x = $668
Now we can solve for x by subtracting $490 from both sides:
$89x = $668 - $490
$89x = $178
And finally, dividing both sides by $89:
x = $178 / $89
x = 2 hours
So, 2 hours of labor were required to replace the water pump.
A researcher found that for the years 2011 to 2017, the equation y = -0. 25(x - 2)^2 + 16, models the average of couches sold in Germany, where x is the number of years since 2011 and y is the number of couches sold. During what year was the average of couches sold in Germany the greatest?
The vertex of the parabola is (2, 16). This means that the average of couches sold in Germany was the greatest in the year 2013, which is 2 years after 2011.
The equation y = -0.25(x - 2)² + 16 models the average of couches sold in Germany, where x is the number of years since 2011 and y is the number of couches sold. We can find the year when the average of couches sold in Germany was the greatest by finding the maximum value of the equation.
To find the maximum value, we can first rewrite the equation in vertex form: y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
y = -0.25(x - 2)² + 16
y = -0.25(x² - 4x + 4) + 16
y = -0.25x² + x + 15
To find the vertex of the parabola, we can use the formula h = -b/2a and k = f(h), where f(h) is the value of y at the vertex.
h = -b/2a = -1/(2*(-0.25)) = 2
k = f(h) = -0.25(2)² + 2 + 15 = 16
Therefore, the vertex of the parabola is (2, 16). This means that the average of couches sold in Germany was the greatest in the year 2013, which is 2 years after 2011.
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How to factorize and get the answer?
make brainalist keep smiling dude..!
draw an angle of 65° and draw an angle equal to this angle, using ruler and compass
The Construction of angle equal to 65 degree is shown below with attached figure.
What is Construction?Geometric constructions are precise drawings of geometrical shapes, angles, and lines. We will need a pencil, a ruler (or other straight edge), and compasses to do this. Perpendicular bisector and angle bisector are the fundamental constructs.
The steps to draw angle 65 and copy of Angle:
(i) Draw ∠AOB = 65° with the help of protractor.
(ii) Draw a ray O’X.
(iii) With O as center and any radius, draw an arc cutting OA and OB at C and D respectively.
(iv) With O’ as center and with the same radius, draw an arc, cutting O’X at P.
(v) With P as center and radius equal to CD, cut the arc through P at Q.
(vi) Join O’Q and produce it to Y. Then ∠YO’X is the required angle equal to ∠AOB.
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how do i do this question
Answer:
Step-by-step explanation:
i9 have no idea sorry
Which additional fact would prove that quadrilateral WXYZ is a parallelogram?
here is a quadrilateral WXYZ in which side XY is parallel to side WZ.
A. XY = YZ
B. m∠X + m∠Y = 180°
C. YZ = WX
D. m∠Y ≅ m∠W
The extra information "XY = YZ" would demonstrate that the parallelogram WXYZ is a parallelogram.
The parallelogram theorem is what?Theorem: The area of a triangle is roughly half the area of a parallelogram if they share a base and are situated between the same parallels.
These bisectors meet at a 90-degree angle.
And it indicates that they are parallel.
We discover that there are four congruent triangles, with XY parallel to WZ and WX parallel to YZ even though they are perpendicular to one another.
In addition, contrasting angles are equal.
The properties of the parallelogram are these two latter results.
Therefore, the additional fact "XY = YZ" would demonstrate that the triangular WXYZ is a parallelogram.
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Kathy is organizing her desktop, which measures 22 inches by 4 feet. What is the area of Kathy’s desktop?
The area of any other shape can be broken down into smaller rectangles and the area of each rectangle can be calculated and added together to get the total area.
Kathy is organizing her desktop, which measures 22 inches by 4 feet. To calculate the area of Kathy’s desktop, we can use the formula for area, which is length multiplied by width. In this case, the length is 4 feet and the width is 22 inches. To make the measurements easier to work with, we can convert the length into inches. There are 12 inches in a foot, so 4 feet is equal to 48 inches. Now, the length of Kathy’s desktop is 48 inches and the width is 22 inches. To calculate the area, we multiply the length (48 inches) by the width (22 inches). The area of Kathy’s desktop is 1,056 square inches.
To further explain the concept of area, it is the amount of two-dimensional space that a shape takes up. It is measured in square units, such as square inches, square feet, or square yards. To calculate the area of any shape, you need to know its length and width. To calculate the area of a rectangle, you multiply the length by the width. The area of any other shape can be broken down into smaller rectangles and the area of each rectangle can be calculated and added together to get the total area.
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sita wants to filled the ice cream cone with chocolate cream making hemisphere tops for this she bring some cones each of having based diameter 4.2 cm and slant height 7.5cm and a cone of cream with capacity of 800 cm .how many cones can be enough
Each cone has a volume of around 60 [tex]cm^{3}[/tex]. As a result, 800 [tex]cm^{3}[/tex] of cream would be sufficient to fill around 13 cones.
What is a volume?The quantity of space that an item or substance occupies is measured by its volume. Typically, it is expressed in cubic quantities like cubic metres or cubic feet. Volume is frequently used to describe liquids, gases, or other pourable materials like a cup of water or a gallon of fuel. The capacity of a container, such as a tank or box, is also determined by volume.
In this question, the volume of a cone is given by the formula:
V = (1/3)π[tex]r^{2} h[/tex]
Where r is the radius of the base and h is the slant height.
In this case, the radius of the base is equal to half the base diameter (4.2/2 = 2.1 cm) and the slant height is 7.5 cm.
So, the volume of each cone is (1/3)π x (2.1)2 x 7.5 = 28.7 cm3
Therefore, the number of cones needed to fill the ice cream cone with 800 cm3 of cream is 800/28.7 = 27.9 (rounded up to 28).
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for the study of jordanian children in exercise 64, the sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl. (a) calculate the test statistic. (b) find the p-value using table b. then obtain a more precise p-value from your calculator
The sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl. The test statistic is 50 and then the p-value is 32.93
Mean is the ratio of the sum of all observations to the number of observations. Standard deviation is the measure in which it shows how much the variation such as spread, dispersion, from the mean exists and the study of jordanian children in exercise 64, the sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl.
For the study of jordanian children in exercise 64, the sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl.
Given that, exercise n =64
mean = 11.3 mg/dl
standard deviation = 1.6mg/dl
The test statistic is 50
the p-value is calculated by, (n-mean) / (standard deviation)
(64 - 11.3) / (1.6)
32.93
Therefore, the p-value in which it obtains a more precise value is 32.93
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How long will it take someone to knit a scarf that is 160 cm long?
If Pat can knit 2cm in 35 minutes, then would take Pat approximately 2800 minutes to knit a scarf that is 160cm long.
If Pat can knit 2cm in 35 minutes time
then she can knit 1cm in (35/2) minutes, or 17.5 minutes.
To determine the total time to knit a 160cm scarf
Pat would need to work a total of
160cm x 17.5 minutes/cm = 2800 minutes.
Hence,
It would take Pat approximately 2800 minutes to knit a scarf that is 160cm long. This is equivalent to about 46.7 hours or 1.94 days of work
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Pat is knitting a scarf . On average she can knit 2cm in 35mins. How long will take her to knit a scarf that is 160cm long?
The local ferry takes cars across a bay. One day, the ferry transported a total of 610 cars over a 5 -hour period. The ferry took the same number of cars each hour. How many cars did it take each hour? Complete the bar diagram to help.
___ cars
c
c
c
c
___________
c
Answer:122 cars per hour
Step-by-step explanation:Get the total number of cars 610 get the time period 5 hours divide 610 divided by 5 equals 122 cars per hour.
Answer: the ferry took atleast 3,050 cars each hour
Help ASAP! PLEASE HELP ME!
The solution is Option A.
The conversion factor should have gallons in the denominator and the equation will be 350 gallons = 92.3 L
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the amount of gallons of water be = 350 gallons
And , 1 gallon = 3.79 liters
So , the amount of 350 gallons = ( 350 ) x ( 1/3.79 ) L
Substituting the values in the equation , we get
The amount of 350 gallons = ( 350 / 3.79 ) L
On simplifying the equation , we get
The amount of 350 gallons = 92.3 L
Therefore , while converting the gallons to liters , the factor of gallons should be in the denominator
Hence , the equation is 350 gallons = 92.3 L
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Pls show your work thank you will mark the Brainliest
Answer:
12.3
Step-by-step explanation:
take x=0 because intercept means cutting the y axis when x=o
Answer:
Step-by-step explanation:
7
Write the exponential function that describes the situation.
The initial amount of the function is 12, and then it decreases by a factor of 7/9
with each unit increase in x.
Writing Find the length of the hypotenuse of the right triangle. Use pencil and paper. Explain how you can interpret the Pythagorean Theorem using the areas of squares.
Answer:
The length of the hypotenuse is 17.
Nina buys a new rug that matches three colors in her bedroom. The rug is a rectangle. There are eight squares on the rug. Four-eighths of the squares are green. One-fourth of the squares are purple. Are there more green squares or purple squares on the rug? The rest of the squares are blue. How many blue squares are on the rug? Use numbers and symbols to show your mathematical thinking
PLEASE HELP I HAVE 3 MINUTES
100 POINTS
Answer: More green squares. Also 3 blue squares on the rug.
Step-by-step explanation:
The question said the rug is a rectangle. There are also 8 squares on the rug. 4 squares are already taken by green squares. Proof of this is in the fraction itself: 4/8. so out of 8 squares, green occupies 4. We now have 4 squares left.
Purple occupies 1/4. That means we now have 3 squares left. Therefore, the remaining 3 squares are blue.
Answer: 3 blue squares.
In fraction terms, blue occupies 3/8ths of the rectangular rug.
During its first month of business, Dig the Dogs, Inc. purchased $900 of hotdogs of which it paid $300 and owes the rest. During the month, it sold 3/4 of its inventory for $1,000 on account. What is the amount of Cost of Goods Sold for the month ended?
Cost of goods sold (COGS) is an important accounting calculation that measures the costs associated with selling a company’s goods or services. Therefore, the cost of goods sold for the month ended is $600.
Cost of Goods Sold (COGS) is a measure of the cost of goods sold during the accounting period. It is calculated by subtracting the beginning inventory from the cost of goods purchased during the accounting period and then adding the ending inventory. For Dig the Dogs, Inc., the cost of goods sold for the month ended is calculated as follows: Beginning Inventory = 0 Cost of Goods Purchased = $900 Ending Inventory = $300 .COGS = Beginning Inventory + Cost of Goods Purchased - Ending Inventory = 0 + 900 - 300 = $600 Therefore, the cost of goods sold for the month ended is $600.
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A survey was done that asked employees to indicate whether they ride a bicycle or drive to work, and whether they live up to 5 miles or more than 5 miles from work. What is the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle? Enter your answer, rounded to the nearest whole percent, in the box
The probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.
To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we need to use the data from the survey. Let's assume that the survey results are summarized in the following table (attached) :
From this table, we can see that the probability of a worker living more than 5 miles from work is 35%. We can also see that the probability of a worker riding their bicycle is 50%, and the probability of a worker living more than 5 miles from work and riding their bicycle is 20%.
To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we can multiply the probabilities of these two events:
P(Lives > 5 miles and Rides Bicycle) = P(Lives > 5 miles) x P(Rides Bicycle | Lives > 5 miles)
= 35% x (20%/35%)
= 0.5714 or 57% (rounded to the nearest whole percent)
Therefore, the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.
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Please help thank you
The tension forces are 1895 N and 2542 N.
What is the tension in the ropes?
Tension force is a type of force that results from the stretching or pulling of an object, such as a rope, cable, or string. When an object is under tension, it experiences a force that acts along its length, pulling it apart
We know that the third angle in the triangle that is formed is;
180 - [35 + 48]
= 97 degrees
We then have the tension in the ropes as T1 and T2
Using the sine rule;
T1/sin 35 = 3275/sin97
sin97T1 = 3275 sin 35
T1 = 3275 sin 35/sin97
T1 = 1895 N
For T2
T2/sin48 = 3275/sin97
sin97T1 = 3275 sin 48
T1 = 3275 sin 48/sin97
T1 = 2542 N
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when the results of a t test are reported, the following values are also reported: select one: a. median, mode and standard deviation. b. mean, standard deviation and degrees of freedom (df). c. mean, median and standard deviation. d. mean, median and degrees of freedom (df).
The values typically reported when presenting the results of a t-test are: mean, standard deviation, and degrees of freedom (df). Therefore, the correct answer is b.
The mean, standard deviation and degrees of freedom (df) are often shown together with the t-value and p-value when the outcomes of a t-test are reported.
The central tendency and variability of the sample data under analysis are revealed by the mean and standard deviation. Determine the critical values for the t-distribution by using the degrees of freedom (df), which stands for the number of independent observations utilised in the t-test.
These statistics, along with the t-value and p-value, offer crucial details regarding the strength and significance of the relationship or difference under study in the t-test.
Therefore, the correct answer is b. mean, standard deviation and degrees of freedom.
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U={ positive integer between 9 and 21} P={odd numbers} Given that P and Q are subsets of U a. List all the members of P, Q and U b. Illustrate the information on a Venn diagram c. Find P1 and Q1
The set of the numbers are all integers from 9 to 21 inclusive
What is a set?It is the collection of items to form a group
All the members of:
P={odd numbers}
P={9,11,13,15,17,19,21}
Q={Even numbers}
Q= {10,12,14,16,18,20}
U={ positive integer between 9 and 21}
This means that U = {9,10,11,12,13,14,15,16,17,18,19,20,21}
Therefore, P1 and Q1
P prime include all the elements in the universal set that are not in the subset P = {10,12,14,16,18,20}
and Q prime include all the elements in the universal set that are not in subset Q = P={9,11,13,15,17,19,21}
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The thermostat in Steffi’s storage room is set to 56°F. The actual temperature variance in her house can be modeled by the inequality |t − 56| ≤ 3. Plot the range of possible temperatures in her storage room.
The range of possible temperatures in Steffi's storage room is between 53°F and 59°F, inclusive.
What is Inequality?
An inequality is a mathematical statement that compares two values, expressing that they are not necessarily equal. It is often represented using one of the following symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
For example, "x > 5" is an inequality that states that the value of x is greater than 5. Similarly, "y ≤ 10" is an inequality that states that the value of y is less than or equal to 10.
Inequalities are commonly used in algebra and other areas of mathematics, as well as in many real-world applications, to express relationships between values that are not necessarily equal.
The inequality |t − 56| ≤ 3 represents all temperatures within 3 degrees of 56°F, including both those above and below 56°F.
We can represent this range graphically as a horizontal line segment centered at 56°F with a length of 6 units (3 units on either side of 56°F).
Thus, the range of possible temperatures in Steffi's storage room is between 53°F and 59°F, inclusive.
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Similar Triangles Question
Solve for x and determine the scale factor. Notice the change in angles.
X = _____
Scale Factor = _____
Write the answer as a decimal.
Example: 0.3. Must have a 0.
For the given similar triangles, the value of x is 3 and the scale factor is 1/2. This is found using properties of similar triangles.
What is meant by similar triangles?
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. The ratio of the triangles' matching sides is known as the scale factor. The scale factor has no theoretical upper bound, and any ratio between the corresponding sides (not angles) of related triangles is possible.
Given the triangles, ΔAEB and ΔDEC are similar.
Since they are similar triangles,
∠EAB = ∠DCE ( alternate angles)
∠ABE= ∠CDE (alternate angles)
AB = DC (Given)
According to the properties of similar triangles,
AE/EC = BE/ED
4/2 = 6/X
X = 3
Scale factor = ratio of corresponding sides = EC/AE = 2/4 = 1/2
Therefore for the given similar triangles, the value of x is 3 and the scale factor is 1/2.
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what can we conclude from the five number summary about the location of the 20th percentile? the 90th percentile?
By knowing the five number summary of a data set, we can make inferences about the location of specific percentiles within the data.
The five number summary is a way to summarize the distribution of a set of data by providing information about its minimum, first quartile (25th percentile), median (50th percentile), third quartile (75th percentile), and maximum. Using this summary, we can infer information about the location of specific percentiles.
For the 20th percentile, we can conclude that it lies between the minimum and the first quartile. The 20th percentile represents the value below which 20% of the data falls, so it must be less than or equal to the first quartile, which is the value below which 25% of the data falls. It must also be greater than or equal to the minimum.
For the 90th percentile, we can conclude that it lies between the third quartile and the maximum. The 90th percentile represents the value below which 90% of the data falls, so it must be less than or equal to the maximum, which is the largest value in the data set. It must also be greater than or equal to the third quartile, which is the value below which 75% of the data falls.
In conclusion, by knowing the five number summary of a data set, we can make inferences about the location of specific percentiles within the data.
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if the mean is 9,8,10,x,14 is 11 then find the value of x
The value of x is 14
In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organised in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
To find the mean, add up all the numbers and then divide by the number of numbers
(9+ 8+10+ x+14)/5 = 11
Multiply each side by 5
9+ 8+10+ x+14 = 55
Combine like terms
41 +x = 55
Subtract 41 from each side
x =14
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If Jimmy drove 300 miles at a rate of 50 miles per hour, find the number of hours Jimmy traveled.
Answer:
He drove 6 hours.
Step-by-step explanation:
distance = rate times time
300 = 50t Divide both sides by 50
t = 6
What is the measure of the smallest angle?
(Image)
67°
69°
52°
61°
The measure of the smallest angle is 52 degrees
How to determine the measure of the smallest angle?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The triangle
The sum of angles in a triangle is 180
So, we have
2x + 3x - 11 + 2x + 9 = 180
Evaluate the like terms
7x = 182
So, we have
x = 26
This means that
2x = 2 * 26 = 52
3x - 11 = 3 * 26 - 11 = 67
Hence, the smallest is 52 degrees
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What is the answer to 52+6y-22
Ata school
number of boys : number of girls = 11: 9
There are 124 more boys than girls.
Work out the total number of students at the school.
The total number of students at the school is 1240.
What is Ratio ?
With the dividend or number being divided as the antecedent and the divisor or number that is dividing as the consequent, a ratio compares two quantities by division.
we know that, number of boys : number of girls = 11: 9
Let's assume the number of boys = 11x
and, the number of girls = 9x
similarly, There are 124 more boys than girls
So, number of boys = 124 + number of girls
11x = 124 + 9x
2x = 124
x = 62
So, number of boys = 11 ×62 = 682
number of girls = 9 × 62 = 558
∴ Total number of students is 1240 i.e.(682+558).
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Which equations for the measures of the unknown
angles x and y are correct? Check all that apply.
x = costa
x= sin" E)
x= tan'a
y= sin "(a)
y = cos-'
The correct equations for the measures of the unknown angles x and y are:
x = cos(a), y = sin(a).
The trigonometric functions (sin, cos, tan) are mathematical functions that describe the relationships between the sides and angles of a right triangle. Given an angle a in a right triangle, we can use these functions to find the values of the side ratios for that angle. For example:
sin(a) = opposite side / hypotenuse
cos(a) = adjacent side / hypotenuse
tan(a) = opposite side / adjacent side
In these expressions, "opposite side" refers to the side opposite the angle a, "adjacent side" refers to the side adjacent to the angle a, and "hypotenuse" refers to the longest side in the right triangle (the one opposite the right angle).
The inverse trigonometric functions[tex](sin^-1, cos^-1, tan^-1)[/tex] are the reverse of the trigonometric functions. Given a value of a trigonometric function, the inverse function returns the measure of the angle (in radians) for which that value is the result. For example:
[tex]sin^-1(y) = a (where y = sin(a))cos^-1(x) = a (where x = cos(a))tan^-1(t) = a (where t = tan(a))[/tex]
So, the correct equations for the measures of the unknown angles x and y are:
[tex]x = cos^-1(x)y = sin^-1(y)[/tex]
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A business owner wants to have the front window of her store painted and is considering two artists for the job. Suzie has quoted a flat rate of $250 for the job. Jane's quote is $40 per hour, plus $50 to cover the cost of materials. Depending on how long it takes Jane to paint the window, these two could end up charging the same amount. How long would Jane have to take? Write a system of equations, graph them, and type the solution.
Jane would take 5 hours painting the window so both of them could end up charging the same amount
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
Let y represent the total charge for working x hours.
Suzie has quoted a flat rate of $250 for the job. For Suzie:
y = 250
Jane's quote is $40 per hour, plus $50 to cover the cost of materials. For Jane:
y = 40x + 50
For the two to charge the same amount:
250 = 40x + 50
40x = 200
x = 5 hours
Jane would spend 5 hours painting the window.
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