Answer:
3
Step-by-step explanation:
Solving a Real-World Problem
Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is
worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each
point value are on the test.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
x + y = 29, 5x + 2y = 100
x + y = 100, 5x + 2y = 29
5x + y = 29, 2y + x = 100
2x + y = 100, 5y + x = 29
Answer:
x + y = 29
5x + 2y = 100
Step-by-step explanation:
Here, we want to set up equations
There are 29 problems, so adding up the number of individual problem types will give 29
x + y = 29 ••••••(i)
Let us work with points now;
x is worth 5 points, y is worth 2 points
Thus, mathematically;
5x + 2y = 100 ••••••••••(ii)
Answer: A. x + y = 29, 5x + 2y = 100 and the other one is B. 14 problems worth 5 points and 15 problems worth 2 points
if the mean of 6 7 13 and 10 is 8 find rangeif the mean of 67 13 and 10 is 8 find range
Answer:
The range is: 7
Step-by-step explanation:
Given the data set
6, 7, 13, 10
Sorting in ascending order
6, 7, 10, 13
We know that the range is the difference between the highest and lowest values in a set of numbers.
Here:
Highest Value = 13Lowest Value = 6Thus,
Range = Highest Value - Lowest Value
= 13 - 6
= 7
Therefore, the range is: 7
Joel has a prepaid phone card that charges $0.50 to connect and $0.50 per minute. He also can use a cell phone that charges $2.50 to connect and $0.25 per minute. In how many minutes will calls made using the phone card and the cell phone cost the same?
Answer:12 minutes
Hope this is right sorry if not <3
Aiden cuts a ball of string into 14 equal pieces. The length of each piece of string is 2 1/4 yards. What is the original length of the ball of string?
Answer:
31 1/2 yards
Step-by-step explanation:
In order to calculate the original length of the ball of string we simply need to multiply the length of each piece of string by the total number of strings that were produced from the original ball of string. First, we can turn the 2 1/4 into a single decimal number. Since 1/4 is equal to 0.25 we just add this to 2 to get 2.25, now we can go ahead and multiply this by the 14 total pieces.
2.25 * 14 = 31.5 or 31 1/2 yards
Regina carns $7.25 per hour for babysitting her little sister how many hours must Regina work to earn $464
Answer:
64
Step-by-step explanation:
464 / 7.25 = 64
Judy is selling small candles at the fair for $4 each and large candles for $6 each. She collected $144 selling a
total of 28 candles. How many of each candle did she sell? Use x for the small candles and y for the large
candles.
mr martin has 36 calculators in a box. The ratio of the ordinary calculators to the scientific 5:1. How many of each calculator does he have
Answer:
180 calculators.
Step-by-step explanation:
She has 180 calculators because if you were to un - simplify 5:1 you would get 180:5 and you would use the first number. So, you have 180 calculators.
Sorry if this is wrong I tried my best.
Find the measure of the numbered angle
Answer:
1 = 50°, 2 = 130°, 3 = 50°, 4 = 130°, 5 = 40°, 6 = 140°, 7 = 90°, 8 = 140°
Step-by-step explanation:
The sum of the angles of a triangle is 180°. A flat angle measures 180° as well.
Angle 1: 180 - 90 - 40 = 50°
Angle 2: 180 - 50 = 130°
Angle 3: 180 - 130 = 50°
Angle 4: 180 - 50 = 130°
Angle 5: 180 - 90 - 50 = 40°
Angle 6: 180 - 40 = 140°
Angle 7: 180 - 90 = 90°
Angle 8: 180 - 40 = 140°
It's a little complicated, but I hope this helps!
8x-5y=-118x−5y=−118, x, minus, 5, y, equals, minus, 11 xxx-intercept: \Big((left parenthesis ,,comma \Big))right parenthesis yyy-intercept: \Big((left parenthesis ,,comma \Big))
You have two regular polygons
A & B
. The ratio of the interior angles of
A & B
is
21: 22
. The ratio of the exterior angles is
3:2
. How many sides does each polygon have?
Answer:
First polygon has 16 sides
Second polygon has 24 sides
Step-by-step explanation:
Let the number of sides for first polygon be a and that for the second polygon be b
formula for sum of interior angle is;
180n-360
So for individual interior angle we have;
(180n-360)/n
So for polygon A
(180a-360)/a
For polygon B
(180b-360)/b
Let’s divide both to equate to the ratio
(180a-360/a)/(180b-360)/b) = 21/22
Factor out 180
(a-2)/a * b/b-2 = 21/22
b(a-2)/a(b-2) = 21/22
22b(a-2) = 21a(b-2) •••••• (i)
For the second part
Sum of exterior angle of any polygon is 360
Individual exterior angle is 360/n
for the first polygon;
360/a ;
For the second 360/b
Thus;
b/a = 3/2
2b = 3a ••••••••(ii)
b = 3a/2
11(2b)(a-2) = 21a(b-2)
11(3a)(a-2) = 21a( 3a/2-2)
33a(a-2) = 21a(3a-4)/2
22a(a-2) = 7a(3a-4)
22a^2 - 44a= 21a^2-28a
22a^2-21a^2+28a - 44a = 0
a^2 + 28a - 44a = 0
a^2 -16a = 0
a(a-16) = 0
a = 0 (which cannot be)
or a-16 = 0
a = 16
Recall;
b = 3a/2
b = 3(16)/2
b = 24
A triangle has a base of two to the third power units and a height of chicken fourth power units what is the area of the triangle
The volume of a cylinder is 176 cm and its height is 11 cm,
What is the length of the cylinder's radius?
Answer:
4cm
Step-by-step explanation:
The volume of the cylinder is the product of the area of the base and the height. In mathematical equation, this can be written as,
V = πr²h
where V is volume, r is the radius, and h is the height.
Substituting the known values from the given,
176π cm³ = πr²(11 cm)
BRAIN TWISTER/6TH GRADE MATH
Create (1) mathematical problem or mathematical sentence where the answer is "46". For the variables, use t = 3 and h= 5 or t and h for equations.
On a long hike, Greg forgets to fill his canteen. Fortunately, Harold has 40 ounces of water and jake has 60 ounces. The three hikers share water so that each gets an equal amount. At the end of the hike, Greg gives Harold and Jake $5 to split for the water they gave him. How much should Harold and Jake get?
Answer:
Jake should get $3 because he would have given more water since he had the most out of all of them. Harold should get $2 because he gave less water
Step-by-step explanation:
The amount that Harold and Jake will get is $2 and $3, respectively.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Harold has 40 ounces of water, which is needed to be shared among the three, therefore, the amount of water that each of the three will get is,
Amount of water = Total water / Number of persons
= 40 ounces of water / 3 person
= (40/3) ounces per person
Thus, Greg will get (40/3) ounces of water from Harold.
Similarly, Jake has 60 ounces of water, which is needed to be shared among the three, therefore, the amount of water that each of the three will get is,
Amount of water = Total water / Number of persons
= 60 ounces of water / 3 person
= (60/3) ounces per person
Thus, Greg will get (60/3) ounces of water from Harold.
Further, Harold and Jake will get the money in the ratio of the amount of water they shared, therefore, we can write,
(40/3)x + (60/3)x = $5
(40x + 60x)/3 = 5
100x = 5 × 3
x = 15/100
Furthermore, the money each of two will get is,
Amount that Harold will get,
(40/3)x
= (40/3) × (15/100)
= $2
Amount that Jake will get,
(60/3)x
= (60/3) × (15/100)
= $3
Hence, the amount that Harold and Jake will get is $2 and $3, respectively.
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To complete a planter box, mr. Michaels will purchase cedar boards that are 2 inches wide and 8 inches long. He will need to cut down the length of the boards into pieces that are 1 1/3 inches long. How many pieces can mr. Michael cit from each 8 inch board so he can determine how many he will need to purchase?
Answer:
6 pieces
Step-by-step explanation:
Since Mr. Michaels need to cut down the 8 inch long boards into pieces that are 1¹/₃ inches long, the number of pieces he can cut out from the 8 inch long board that are 1¹/₃ inches long is 8 ÷ 1¹/₃ = 8 ÷ 4/3
= 8 × 3/4
= 2 × 3
= 6
So, Mr. Michaels can cut 6 pieces that are 1¹/₃ inches long from the 2 inches wide and 8 inches long board.
Select the correct answer. What is the solution of
[tex] \frac{5}{2}x - 7 = \frac{3}{4}x + 14[/tex]
A. x = -6
B. x = 6
C. x = 8
D. x = 12
Answer:
Option D
Step-by-step explanation:
[tex] \frac{5x}{2} - 7 = \frac{3x}{4} + 14[/tex]
[tex] = > \frac{5x}{2} - \frac{3x}{4} = 14 + 7[/tex]
[tex] = > \frac{7x}{4} = 21[/tex]
[tex] = > x = \frac{21 \times 4}{7} = 12[/tex]
For the equation 2x + 7 =30, x = 3
O True
O False
Answer: False
=============================================================
Explanation:
To see if the x value is a solution or not, we plug it into the equation given
2x+7 = 30 .... original equation
2*3 + 7 = 30 .... replace every x with 3, since we claim that x = 3
6 + 7 = 30 .... multiply 2 and 3 to get 6
13 = 30 ...... add 6 and 7 to get 13
We get two different numbers on either side, so the last equation is not true. We get a contradiction or false statement. So the original equation is false when x = 3. Therefore, x = 3 is not the solution.
That's why the overall claim is false.
Myra gets paid at home for doing extra chores. Last week, she did 5 loads of laundry and 8 loads of dishes, and her parents paid her $18. The week before, she finished 4 loads of laundry and 6 loads of dishes, earning a total of $14. How much does Myra earn for completing each type of chore?
Answer: Laundry = $2
Dishes= $1
Step-by-step explanation:
Let the amount paid for doing laundry be x
Let the amount paid for doing dishes be y.
Based on the information in the question, this can be formed in an equation as:
5x + 8y = 18 ..... i
4x + 6y = 14 ...... ii
Multiply equation i by 4
Multiply equation ii by 5
20x + 32y = 72 ...... iii
20x + 30y = 70 ...... iv
Subtract iv from iii
2y = 2
y = 2/2 = 1
Dishes cost $1
Since 5x + 8y = 18
5x + 8(1) = 18
5x = 18 - 8
5x = 10
x = 2
Laundry cost $2
Find each function value f(-7) if f(x) = 3x + 6
Answer:
-15
Step-by-step explanation:
3*-7=-21+6=-15
Answer:
Step-by-step explanation:
first multiply -7 and 3 since -7 is the element of the function (x)
then you should get (-21)
now add 6 and you answer should be (-15)
Can y’all Plz help me ??(Show ya work) It Says What Value of X makes this equation true
Answer:
[tex]0.6x - 0.1x = 7 + 5 \\ 0.5x = 12 \\ x = \frac{12}{0.5} = 24[/tex]
ILL MAKE BRAINLEST YOUR GONNA HAVE TO ZOOM IN BUT AM I RIGHT
find the values of z and y plssss
Answer:
z is 23 and i dont see a y
Step-by-step explanation:
Please help!
And explain the answers too!
what is 5000000000000000times 409458374.9394ir
Answer:
2,047,291,874,697,000,000,000,000
Step-by-step explanation:
that is the answer to the multiplication statement xD
whats three hundred x three hundred 300x300
Answer:
90000
Step-by-step explanation:
this baby has big brain
someone please help
f(x) = 2x2 - 5
and
g(x) = 5x + 7
Find
f(g(x)) = [ ? ]x2 +[ ]x + [ ]
9514 1404 393
Answer:
f(g(x)) = 50x² +140x +93
Step-by-step explanation:
Put the function argument in place of x and simplify.
f(g(x)) = f(5x+7) = 2(5x+7)² -5
= 2(25x² +70x +49) -5
f(g(x)) = 50x² +140x +93
_____
We took advantage of the knowledge that ...
(a + b)² = a² +2ab +b² . . . . . where a=5x and b=7
what is it plz ????????????
The side length of aDavid is a statistician. He has a sample size of 40 (which he cannot change). What element of his hypothesis test can he adjust to minimize the probability that he incorrectly rejects the null hypothesis?
the mean of the population
the mean of the sample
the standard deviation of the population
the significance level of the testn equilateral triangle is 6 cm. What is the height of the triangle?
Answer: D) the significance level of the test
=======================================================
Explanation:
The significance level of the test, also known as "alpha", is the probability of making a type 1 error. A type 1 error is where you reject the null hypothesis but it was true all along.
The null hypothesis is where we test a certain probability distribution (eg: normal distribution). Specifically we gather a sample of values and compute the test statistic. If the probability of getting that test statistic or more extreme is smaller than alpha, then we reject the null. This probability value is known as the p-value.
If you lower the alpha value, then that will make it more likely you do not reject the null. Consider an example where alpha = 0.10 to start with. If you get a p-value of 0.02, then you would reject the null. The same would apply for alpha = 0.05; however, with alpha = 0.01, the p-value is no longer smaller than alpha. At this point we do not reject the null. Your textbook may use the phrasing "fail to reject the null".
Going in the opposite direction, increasing the alpha value will make it more likely to reject the null. Each time you adjust the alpha value, keep the p-value to some fixed number (between 0 and 1).
The height of the equilateral triangle is 3√3 cm.
What is hypothesis testing?Hypothesis testing is a statistical method that is used to make decisions about a population based on a sample of data.
It involves testing a null hypothesis (H0) against an alternative hypothesis (Ha) using statistical techniques.
We have,
To minimize the probability of incorrectly rejecting the null hypothesis in a hypothesis test with a fixed sample size of 40, the statistician can adjust the significance level of the test.
The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is actually true.
By choosing a smaller significance level, the statistician can decrease the probability of making a Type I error (rejecting the null hypothesis when it is actually true).
However, decreasing the significance level also increases the probability of making a Type II error (failing to reject the null hypothesis when it is actually false).
Therefore,
The choice of significance level involves a trade-off between the two types of errors and should be based on the specific context of the problem and the consequences of each type of error.
Now,
The height of an equilateral triangle can be found using the formula:
height = (side length / 2) x √3
The side length = 6 cm
So,
height = (6 / 2) x √3
= 3√3 cm
Therefore,
The height of the equilateral triangle is 3√3 cm.
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Please Answer! This is urgent!
Step-by-step explanation:
If the perimeters could be equal,
then 4(x + 3) = 2(x + 4 + x + 1).
=> 4x + 12 = 2(2x + 5)
=> 4x + 12 = 4x + 10
However 12 =/= 10 for all real values of x. Hence their perimeters can never be equal.
Nick and eddie are both thinking of a number. Eddies number is 3/7 of nicks number. There is a difference of 52 between their two numbers. What are the two numbers
Answer:
nick's number = 91
eddie's number = 39
Step-by-step explanation:
n = nick's number
[tex]\frac{3}{7}[/tex]n = eddie's number
[tex]\frac{7}{7}[/tex]n - [tex]\frac{3}{7}[/tex]n = 52
[tex]\frac{4}{7}[/tex]n = 52
cross-multiply: 4n = 52(7)
4n = 364
n = 364/4 = 91
eddie's number: [tex]\frac{3}{7}[/tex] · 91 = 273/7 = 39
Nick's number is 91
Eddie's number is 39
What is expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.
Coefficient: A coefficient is a number that is multiplied by a variable in an expression.
Given,
Eddie's number is 3/7 of Nick's number
Let Nick's number be x
Then Eddie's number = 3x/7
Difference of the numbers is 52
x - 3x/7 = 52
(7x - 3x)/7 = 52
4x/7 = 52
4x = 52×7
x = 364/4
x = 91
Another number = 3x/7
= 3(91)/7
= 3 × 13
= 39
Hence, 91 is Nick's number and 39 is Eddie's number.
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