a.) [tex]135 + 89 + \text{C} \geq 325[/tex]
[tex]224 + \text{C} \geq 325[/tex]
b.) [tex]224 + \text{C} \geq 325[/tex]
[tex]\text{C} \geq 325 - 224[/tex]
[tex]\text{C} \geq 101[/tex]
find the misding values in the ratio table then write the equivalent ratios forks 16 8 spoons 10, 30
The missing number in the ratios of numbers are 16:10 8:20 and 0:30
How to determine the missing numbers?Ratios are quantitative relationships between two numbers that describe how many times one value can contain another
the given parameters are
Forks 16 8 ----
Spoons 10 --- 30
The numbers are written in ascending order of magnitude
Using AP,
for forks: a = 16, 2nd term = 8
common difference = 8-16 - -8
For spoons a = 10, 3rd term = a + 2d = 30
30 = 10 + 2d
30 -10 = 2d
d= 20/2 = 10
Therefore the 2nd term = 10+10=20
The table reappears as follows
Forks 16 8 0
Spoons 10 20 30
Therefore the equivalent ratios are 16:10 8:20 and 0:30
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Which angles are congruent to each other? Select all that apply.
Answer:
1,2, and 4
Step-by-step explanation:
vertical angles theorem, which says that the vertical angles that are formed when two lines intersect are congruent.
Johan wants to make some small cakes.
He finds a recipe that says he needs 360 grams of flour to make 15 small cakes.
Johan has 0.85 kg of flour.
Johan works out how much flour he would need to make 38 small cakes, using the
information given in the recipe.
Does Johan have enough flour, according to the recipe, to make 38 small cakes?
Show your working clearly.
The amount of flour that will be needed for 38 cakes is 912 grams therefore Johan does not have enough amount of flour
What is word problem?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
360 grams is needed for 15 small cakes
therefore for 1 small cake, 369/15 = 24grams will be needed
therefore for 38 small cakes = 38× 24 = 912 grams of flour will be needed.
Johan has 0.85 kg of flours which is equivalent to 0.85 × 1000grams = 850 grams of flour.
Since 912 grams will be needed for 38 small cakes , it shows that Johan does not have enough amount of flour for 38 small cakes.
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Apiece of Wire 80cm long is cut into the two parts and bent each part to Form a square the tota area of the two squaresquare is 250 Find perimiter of each Square side length of each Square
The perimeter of the square with side of 5 cm is 20 cm.
The perimeter of the square with side length of 15 cm is 60 cm.
What is the area of each square?The area of each square is calculated as follows;
Let the dimension of first square = x
Let the dimension of second square = y
x² + y² = 250 ---- (1)
4(x + y) = 80 ----- (2)
x + y = 80/4
x + y = 20
x = 20 - y
Substitute x in equation (1)
(20 - y)² + y² = 250
400 - 40y + y² + y² = 250
2y² - 40y + 150 = 0
y² - 20y + 75 = 0
solve for y, using formula method;
y = 15 or 5
Solve for x;
x = 20 -15 = 5 or
x = 20 - 5 = 15
The perimeter of first = 4x = 4 x 5 = 20 cm
The perimeter of the second = 4y = 4 x 15 = 60 cm
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Segment AB is perpendicular to the circle centered at O. The length of AB is 2.5 units and the length of CB is 1.5 units. Find the exact length of the radius of this circle.
The exact length of the radius of this circle is 2.69 units.
Given that, the length of AB is 2.5 units and the length of CB is 1.5 units.
Since AB is perpendicular to the circle, the triangle ABC is a right triangle. By the Pythagorean theorem, the radius of the circle can be found by solving:
r² = (2.5)² + (1.5)²
r² = 7.25
r = √7.25
r = 2.69 units
Therefore, the exact length of the radius of this circle is 2.69 units.
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PLEASE I NEED AN ANSWER QUICKLY
Let c = children's and a = adults.
Mathland Theatre charges $5.00 for children's tickets and $9.00 for adult tickets. One night the theatre sold 290 tickets and took in $2250. How many of each type of ticket were sold?
The number of children ticket sold is 90 while the number of adult ticket sold is 200.
How to find the number of each type of ticket sold?Math land theatre charges $5.00 for children's tickets and $9.00 for adult tickets. One night the theatre sold 290 tickets and took in $2250.
Therefore, let's find the number of each type of ticket sold as follows:
Hence,
Let
c = children's ticketa = adult ticketsTherefore, using equation,
c + a = 290
5c + 9a = 2250
Multiply equation(i) by 5
5c + 5a = 1450
5c + 9a = 2250
subtract the equation
4a = 800
divide both sides by 4
a = 800 / 4
a = 200
Therefore, let's find c
c = 290 - 200
c = 90
Hence,
number of children's ticket = 90
number of adult tickets = 200
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On a recent math test, the mean score was 75 and the standard deviation 5. What is the 25th percentile for the math scores
The 25th percentile for the math scores is 71.65.
How to determine the 25th percentile for the math scores?In Mathematics and Geometry, the z-score of a given sample size or data set can be calculated by using this formula:
Z-score, z = (x - μ)/σ
Where:
σ represents the standard deviation.x represents the sample score.μ represents the mean score.Note: 25th percentile for the math scores is the same as the first quartile for the math scores.
Based on the z-score table A, 25th percentile (0.25) is equal to a z-score of -0.67;
0.2514 = -0.67
By substituting the parameters, we have:
Z-score, z = (x - μ)/σ
-0.67 = (x - 75)/5
x = 75 - 3.35
x = 71.65
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A health insurance company advertises on television, on radio, and in the local newspaper. The marketing department has an advertising budget of $46,400 per month. A television ad costs $1000, a radio ad costs $200, and a newspaper ad costs $600. The department wants to run 64 ads per month, and have as many television ads as radio and newspaper ads combined. How many of each type of ad can the department run each month?
The number of each type of ad that the department can run each month are:
TV Ads = 32
Radio Ads = 12
News Ads = 20
How to solve Simultaneous equation word problems?x = number of tv ads
y = number of radio ads
z = number of news ads
Two formulas are indicated.
x + y + z = 64
1000x + 200y + 600z = 46400
they want as many tv ads as radio and news ads combined.
equation for that is x = y + z
since x = y + z, replace x with y + z in both equations to get;
y + z + y + z = 64
1000 * (y + z) + 200 * y + 600 * z = 46400
combine like terms and simplify to get:
2y + 2z = 64
1000y + 1000z + 200y + 600z = 46400
combine like terms again to get:
2y + 2z = 64
1200y + 1600z = 46400
Solving simultaneously gives:
y = 12
z = 20
Thus:
x = 12 + 20
x = 32
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Danielle is saving to buy a bedroom set that cost $2,976. If she saves for 24 weeks, how much will she need to save each week?
Answer:
$124 per week
Step-by-step explanation:
To fins how much she needs to save each week, divide the total cost by the amount of time. In this problem, divide $2,976 by 24 weeks to find the amount she needs to save.
$2976/24=$124 per week
What is the probability the he will choose a red marble
The probability that Tom will choose a red marble from the bag is 1/9.
Given that,
Tom is choosing at random from a bag of colored marbles.
Odds in favor = number of success : number of failures
Odds of getting a red marble = 1 : 8
This means that there ratio of red marbles to other marbles = 1 : 8
Number of red marbles = 1
Total number of marbles = 1 + 8 = 9
Probability of choosing a red marble = 1/9
Hence the required probability is 1/9.
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This table shows the percent increase in the consumer price index (CPI) over five three-month periods. A Bar Graph was made to represent this information graphically.
What is wrong with this Bar Graph?
A. The vertical axis is divided into unequal intervals.
B. The vertical axis is too small for this data.
C. The bars are not of the same width.
D. The heights of the bars do not represent the correct percent increase.
Answer:
D
Step-by-step explanation:
to meet slope constraint rhonda wants to change the height of the zip-line 7 ft and end at a height 9 ft above the ground
Test Rhonda’s claim
All the three locations has been checked below.
Using Pythagoras theorem,
12² = 8² + x²
144 - 64 = x²
x= √80
x=8.9
Now, using Trigonometry
tan F = P/B
tan F= 8/8.9
and, sin F = P/H
sin F= 8/12 = 2/3
and, cos F = B/H
cos F= 12/8.9
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1 The Associative Property of Multiplication states that the way terms are grouped when multiplied does NOT change which of the following? The product The factors The order The process Skip 0/10 complete
Answer: THE PRODUCT
Step-by-step explanation:
The associative property of multiplication says that the product of three or more numbers remains the same no mater how the numbers are grouped.
example (3x5x2) is the same as ( 5x2x3) both = 30
What is 0.007 divided by 0.498 to nearest tenth
Answer:
0.0
Step-by-step explanation:
To find 0.007 divided by 0.498, we can perform the following calculation:
0.007 / 0.498 ≈ 0.0141
Rounding this to the nearest tenth gives:
0.0141 ≈ 0.0
Therefore, the result, rounded to the nearest tenth, is 0.0.
A single die is rolled twice. The 36 equally-likely outcomes are shown to the right.
Find the probability of getting two numbers whose sum exceeds .
The probability that the sum exceeds 5 is P ( A ) = 0.6111
Given data ,
To find the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice, we need to count the number of outcomes where the sum of the two numbers is greater than 5, and then divide that by the total number of equally-likely outcomes.
The outcomes where the sum exceeds 5 are:
(2, 4), (2, 5), (2, 6)
(3, 3), (3, 4), (3, 5), (3, 6)
(4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
There are 22 outcomes where the sum exceeds 5 out of a total of 36 equally-likely outcomes.
So, the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice is:
P(sum > 5) = 22 / 36 ≈ 0.6111 or approximately 61.11 %
Hence , the probability is P ( A ) = 0.6111
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The complete question is attached below :
A single die is rolled twice. The 36 equally-likely outcomes are shown to the right.Find the probability of getting two numbers whose sum exceeds 5
Philip finances a new refrigerator.
The function y = 600 - 75x
represents the remaining balance, y,
of the refrigerator purchase after
x months.
The domain and the range of the function are given as follows:
Domain: 0 ≤ x ≤ 8.Range: 0 ≤ y ≤ 600.What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.The function in this problem is given as follows:
y = 600 - 75x.
The input variable x represents the number of months, which cannot be negative, hence the lower bound of the domain is given as follows:
x = 0.
Meaning that the upper bound of the range is of y = 600.
The balance remaining cannot be negative, hence:
The lower bound of the range is of y = 0.The upper bound of the domain is: 600 - 75x = 0 -> x = 600/75 -> x = 8.Missing InformationThe problem asks for the domain and the range of the function.
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HELP ASSAP 20 POinTSSSSSSSSSSSSSS
Step-by-step explanation:
use the formula V=1/3hπr².
V=1/3×3 π 2×2
V=1/3×12π
V=4πcm3
Amelie travelled to her friend's house and her journey is shown on the distance-time graph below. She travelled the final 4 hours of her journey at a constant speed of 60 km/h. Work out the value of d. Distance travelled (km) 270- 0 3 Time (hours) -
The total distance traveled by Amelia to her friend's house is d = 510 miles
Given data ,
Let the distance traveled by Amelia to her friend's house be d
Now , the speed of the final 4 hours of her journey = 60 km/hr
So , the distance traveled in the final 4 hours = 4 x 60 = 240 km
And , the initial distance traveled = 270 km
So , from the graph
The total distance d = 270 + 240
d = 510 miles
Hence , the distance traveled by Amelia = 510 miles
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At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?
Applying the Solution to a 3X3 System
Show up all steps please
A water sample shows 0.056 grams of some trace element for every cubic centimeter
of water. Liam uses a container in the shape of a right cylinder with a diameter of 14
em and a height of 13.6 cm to collect a second sample, filling the container all the
way. Assuming the sample contains the same proportion of the trace element,
approximately how much trace element has Liam collected? Round your answer to
the nearest tenth.
what is the perimeter of a rectangle with corners at (-5, 1) ,
(2, 1) , and (2, -3) ?
Answer:
22
Step-by-step explanation:
length is given by (3--1=4)
width is given by (2--5=7)
perimeter is given by:
P=2l + 2w
P=2(4)+2(7)
P=8+14
P=22
Jared's class took a survey to see how many students owned a trampoline. Of the 24 students in the class, 14 students said they owned a trampoline. If you chose a student at random from Jared's class, what is the probability that the student does not own a trampoline?
The probability that a student chosen at random from Jared's class does not own a trampoline is 5/12.
The probability that the student does not own a trampoline is equal to the number of students who do not own a trampoline divided by the total number of students in the class.
The number of students who do not own a trampoline is equal to the total number of students in the class minus the number of students who own a trampoline:
24 - 14 = 10
Therefore, the probability that a student chosen at random from Jared's class does not own a trampoline is:
P(not owning a trampoline) = 10/24
Simplifying the fraction,
P(not owning a trampoline) = 5/12
Therefore, the probability that a student chosen at random from Jared's class does not own a trampoline is 5/12.
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Solid metal support poles in the form of right cylinders are made out of metal with a density of 5.4 g/cm^3. This metal can be purchased for $0.71 per kilogram. Calculate the cost of a utility pole with a radius of 17.8 cm and a height of 700 cm. Round your answer to the nearest cent. (Note: the diagram is not drawn to scale)
The cost of the utility pole with a radius of 17.8 cm and a height of 700 cm is; $3774.4
How to determine the volume?From the information given, we have the following parameters;
Density = 5.4 g/cm³
Mass = Ikg = 0.71 kg
Cost per mass = $0. 51
Let's determine the volume of this cylinder:
Volume = mass / density
Substitute the values
Volume = 0.71 /5.4
Volume = 0.131 cm³
Thus, 0.131 cm³ costs $0.71
For the utility pole;
Volume = 2 πr²h
Where:
r is 17.8cm
height is 700cm
Volume = 3. 142 × 17.8 × 17.8 × 700
Volume = 696414.32 cm³
If 0.131 cm³ costs $0.71
Then 696414.32 cm³ will cost:
= 696414.32 × 0.71/ 0.131
= 3774.4
Thus, the cost of a utility pole is $3774.4
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A={composite number between 10 and 20} with formula
The composite numbers between 10 and 20 are: 12, 14, 15, 16 and 18 which have more than 2 factors.
To find a composite number, we find the factors of the given number. The best way to determine a composite number is to do a divisibility test. The divisibility test helps us determine if the number is prime or composite. Divisibility means that one number is divided completely (without remainder) by another number.
Last week's and this week's low temperatures are shown in the table below.
Low Temperatures for 5 Days This Week and Last Week
Low Temperatures
This Week (°F)
Low Temperatures
Last Week (°F)
4
10
13 9
6
5
9
6
8 5
Which measures of center or variability are greater than 5 degrees? Select three choices.
O the mean of this week's temperatures
O the mean of last week's temperatures
the range of this week's temperatures
the mean absolute deviation of this week's temperatures
the mean absolute deviation of last week's temperatures
The measures of center or variability are greater than 5 degrees
The the mean of this week's temperatures the mean of last week's temperaturesthe range of this week's temperaturesHow to measure for variablilyThis Week's Mean: (4 + 13 + 6 + 9 + 8) / 5 = 40 / 5 = 8
Last Week's Mean: (10 + 9 + 5 + 6 + 5) / 5 = 35 / 5 = 7
Then the ranges
This Week's Range: (13 - 4) = 9
Last Week's Range: (10 - 5) = 5
The MAD for both weeks
|(4 - 8)| + |(13 - 8)| + |(6 - 8)| + |(9 - 8)| + |(8 - 8)|
= 4 + 5 + 2 + 1 + 0 = 12
This Week's MAD: 12 / 5 = 2.4
|(10 - 7)| + |(9 - 7)| + |(5 - 7)| + |(6 - 7)| + |(5 - 7)| = 3 + 2 + 2 + 1 + 2 = 10
Last Week's MAD: 10 / 5 = 2
Hence the measures of center or variability are greater than 5 degrees are:
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Find the solutions to y = –8x for x = 2, 4, and 8.
A. (–16, 2), (–32, 4), (–64,8)
B. (16, 2), (32, 4), (64,8)
C. (2, 16), (4, 32), (8, 64)
D. (2, –16), (4, –32), (8, –64)
The solutions to y = –8x for x = 2, 4, and 8 are (2, –16), (4, –32), (8, –64), hence, option D is correct.
We are given the equation y = -8x and asked to find the solutions for x = 2, 4, and 8. To find the solutions, we substitute the given values of x into the given linear equation and solve for y.
For x = 2, we have,
y = -8x
y = -8(2)
y = -16
Therefore, the solution for x = 2 is (2, -16).
For x = 4, we have,
y = -8x
y = -8(4)
y = -32
Therefore, the solution for x = 4 is (4, -32).
For x = 8, we have,
y = -8x
y = -8(8)
y = -64
Therefore, the solution for x = 8 is (8, -64).
Putting these solutions together, we get {(2,-16), (4,-32), (8,-64)}. Hence, the correct answer is option D.
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Help me solve and show my work please
The value of the expression is 0.017455065
What is trigonometrical expression?Identities enable us to simplify complicated expressions. They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations.
The given expression is (Tan π/18 + Tan π/9) ÷ (1 - Tan π/1 Tanπ/9)
This gives [Tan (π/18 * π/9) ÷ 1/(Tan(π/18 * π/9)
Simplify further to have
Tanπ²/162 * 162/π²)
This gives Tan1 = 0.017455065
This implies that (Tan π/18 + Tan π/9) ÷ (1 - Tan π/1 Tanπ/9) = 0.017455065
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A right triangle has side lengths 6 centimeters and 8 centimeters. Is it possible for there to be more than one right triangle with whole-number side lengths that includes the given side lengths? Explain.
The given side lengths, 6 cm and 8 cm, satisfy the Pythagorean theorem because $6^2 + 8^2 = 100 = 10^2$, which means that the triangle is a right triangle.
To determine if there is more than one right triangle with whole-number side lengths that includes these given side lengths, we need to check if there exist other pairs of whole numbers that satisfy the Pythagorean theorem and include 6 cm and 8 cm as two of their sides.
Let's call the third side of the right triangle x. Then we have:
62+82=x26^2 + 8^2 = x^262+82=x2
which simplifies to:
36+64=x236 + 64 = x^236+64=x2
100=x2100 = x^2100=x2
x=100=10x = \sqrt{100} = 10x=100
=10
So the only other possible triangle with whole-number side lengths that includes the given side lengths has side lengths of 6 cm, 8 cm, and 10 cm.
Therefore, there is only one other right triangle with whole-number side lengths that includes the given side lengths, and it is unique.
Suppose that the functions f and g are defined as follows.
Find f.g and f+ g. Then, give their domains using interval notation.
The composition of f. g derived from the equations in the attached image is: [tex]\frac{1}{10}(2x + 1)[/tex] and f+g as √(4x-1))/(5x²+3)
How to solve compositionComposition is a mathematical operation that combines two functions to form a new function. From our question, we are given two functions f(x) and g(x).
One of their composition can be represented by f(g(x)).f(g(x)) means function out of g(x) will serve as input x for function f(x). In a more simpler words, f(g(x)) is the function obtained by taking the output of g(x) and using it as the input for f(x).
Using the question given as an example,
For f.g:
Firstly, we have to compute the composition of f and g.
This can be expressed as:
f(g(x))f(g(x)) = f(√(4x-1))= 1/[5(√(4x-1))² + 3]= 1/[5(4x-1) + 3]
= 1/(20x + 10)
= [tex]\frac{1}{10}(2x + 1)[/tex]
For f+g:
To find f+g, we will just add the two functions together as below:
f+g = 1/(5x²+3) + √(4x-1)= (√(4x-1) + (5x²+3)
= √(4x-1))/(5x²+3)
So the answers are;
f.g: = [tex]\frac{1}{10}(2x + 1)[/tex]
f+g = √(4x-1))/(5x²+3)
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Which statement could be made based on the diagram below?
A) m∠3 + m∠6 = 90
B) ∠3 = ∠6
C) ∠3 = ∠5
D) m∠4 + m∠5 = 180
Answer:
A) angle 3 plus angle 6 = 90°
Step-by-step explanation:
just think about it : to the left of m at the intersection with n is 90°. so, to the right it must be 90° too.
because one side of a line represents always 180° for all angles around a single point.