The greatest number of bags Caesar can make is 16 bags. Each of these bags will have 5 boxes of pasta and 8 jars of sauce.
If Caesar made fewer bags, he would have boxes of pasta and jars of sauce remaining.He could use 8 bags but this is not the greatest number he could use.What is the number of pasta and sauce in each bag?Boxes of pasta = 32Jars of sauce = 48Find the greatest common factor of 32 and 48
32 = 1, 2, 4, 8, 16, 3248 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.The greatest common factor of 32 and 48 is 16
So, the greatest number of bags Caesar can make is 16 bags
Number of pasta in each bag = 32/16
= 5 boxes of pasta per bag
Number of sauce in each bag = 48/16
= 8 jars of sauce per bag
If Caesar made fewer bags, he would have boxes of pasta and jars of sauce remaining.
He could use 8 bags but this is not the greatest number he could use.
Therefore, Caesar can use the greatest common factor to determine the highest number of bags he could use.
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The candy jar is only 1/4 full and all three brothers want an equal share. What fraction of the candy jar should each brother get?
Answer: 1/12
Step-by-step explanation: If the candy jar is only 1/4 full, and there's 3 brothers, they would each receive 1/3 of 1/4. THis would be 1/12 of the jar.
a system is tested for faults once per hour. if there is no fault, none will be detected. if there is a fault, the probability is 0.78 that it will be detected. the tests are independent of one another. given that a fault has gone undetected for 2 hours, what is the probability that it will be detected in the next hour? round the answer to two decimal places. numeric response
The probability that it will be detected in the next hour is 0.04.
For a system, a fault test each hour is a Bernoulli with success defined as detecting a fault.
The probability of success is 0.78
Let 'x' denote the number of tests conducted up to and including the test that detected a fault.
Then x* - Geometry (0.78).
The probability mass function of the random variable x is;
P(x) = { P( 1 - P )ˣ⁻¹ x = 1,2, . . .
{ 0 otherwise
The Probability that a fault will be detected on the third hour, given that it has gone undetected during the first two hours is;
P(X = 3 / x = 2) = P(X = 3 and x > 2) / P(x > 2)
= P( x = 3 ) / 1- P(x ≤ 2)
= P( x = 3 ) / 1-P(x = 1) - P(x = 2)
= P(3) / 1-P(1) - P(2)
= (0.78)(0.2)² / 1 - (0·78)(0.2) - (0.78)(0.2)
= (0.78)(0.04) / 1 - (0.78)(0.2) - (0.78)(0.2)
= 0.0312 / 1 - 0.156 - 0.156
= 0.0312 / 0.688
= 0.04
The probability that it will be detected in the next hour is 0.04
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what type of statistics is used to estimate how likely it is that a statistical result based on data from a random sample is representative of the population from which the sample sia sssumed to have been selecteed
We use Inferential Statistics is used to estimate how likely it is that a statistical result based on data from a random sample is representative of the population.
Given that;
What kind of statistics is used to gauge the likelihood that a statistical finding based on information from a random sample is representative of the population the sample is presumed to have been drawn from?
Inferential Statistics:
You attempt to conclude using inferential statistics that go beyond the immediate facts alone. For instance, we use inferential statistics to try to infer what the population would think from the sample data. Alternately, we utilize inferential statistics to assess the likelihood that an observed difference between groups in this study is a reliable one or one that may have occurred by chance. Descriptive statistics are used to simply describe what's happening in our data, while inferential statistics are used to conclude more general conditions from our data.
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For triangle XYZ, m∠X = (5g + 18)° and the exterior angle to ∠X measures (8g + 32)°. Find the measure of ∠X and its exterior angle. Interior angle = 68°; exterior angle = 112° Interior angle = 112°; exterior angle = 68° Interior angle = 73°; exterior angle = 105° Interior angle = 105°; exterior angle = 73°
The interior angle and the exterior angle of triangle XYZ is 68° and 112° respectively.
What is a triangle?
A triangle is a plane shape that has three sides.
Recall that, the sum of a interior angle and an exterior angle of a triangle is 180°.
Using the formula,
a+b = 180°............ Equation 1Where:
a = interior angle b = exterior angle.From the question,
Given:
a = m∠X = (5g + 18)° b = ∠X = (8g + 32)°Substitute these values into equation 1
(5g + 18)+ (8g + 32) = 180Solve for g
13g + 50 = 18013g = 130g = 130/13g = 10Hence, interior angle of X = (5×10)+18 = 50+18 = 68° and exterior angle of X = (8×10)+32 = 80+32 = 112°
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Answer: I belive the answer is A
Step-by-step explanation: i could be wrong
Type the correct answer in the box. If necessary, use / for the fraction bar.
Both pyramids in the figure have the same base area as the prism. The ratio of the combined volume of the pyramids to the volume of the pris
expressed as a fraction in simplest form, is
The ratio of the combined volume of these pyramids to the volume of the prism as a fraction is equal to 1/3.
How to calculate the volume of a pyramid?
The volume of a pyramid can be calculated by using this formula:
Volume = 1/3 × b × h
Where:
h is the height.
b is the base area.
Volume of this prism = 1/2 × b × hHere, both pyramids have the same base area as the prism, their volume is given by:
Volume of a pyramid = (1/3 × b × h) + (1/3 × b × h)
Volume of a pyramid = 2/3 × b × h
Also, the volume of this prism = 1/2 × b × h
Thus, the ratio is given by:
Ratio = (2/3 × b × h)/(1/2 × b × h)
Ratio = 2/3 × 1/2
Ratio = 1/3.
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On Monday, a museum had 500 visitors. On Tuesday, it had 900 visitors. Estimate the percent change in the number of visitors to the museum. Use pencil and paper. Estimate how many people would have to visit the museum on Wednesday to have the same estimated percent change between Tuesday and Wednesday as between Monday and Tuesday. Explain your answer.
The percentage increase regarding the change in visitor is 80%.
How to calculate the percentage?From the information, the museum had 500 visitors and on Tuesday, it had 900 visitors.
It should be noted that the increase in numbers will be:
= 900 - 500
= 400
The percentage increase will be:
= Increase / initial value × 100
= 400/500 × 100
= 0.8 × 100
= 80%
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At the beginning of a chemistry experiment, the volume of liquid in a container was 3 milliliters. During the experiment, the volume dropped to
2.1 milliliters. Find the percent of decrease.
Answer:
30%
Step-by-step explanation:
To calculate the percent of change, you find the amount of change and divide that my the original amount
[tex]\frac{3-2.1}{3}[/tex] = [tex]\frac{.9}{3}[/tex] = .3 As a percent, this would be 30%
Which expression shows the distance you would drive from the library to the grocery store along this road?
The expression that shows the distance you would drive from the library to the grocery store along this road is; |-5|+|7|
How to solve Absolute Value Inequalities?
An absolute value inequality is defined as an expression that has absolute functions as well as inequality signs. For example, the expression |x + 5| > 1 is an absolute value inequality that contains a greater than symbol.
Now, from the inequality line graph attached, we see that the point of the library is at -5 on the line graph.
Similarly, we also see that the point of the grocery store which i will liken to the maths class is at the point 7.
Thus, the distance between both points when we take absolute values into consideration is; |-5|+|7|
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What is the size of an angle called a revolution
Answer:
Step-by-step explanation:
The size of the angle of one whole revolution is 360 degrees. A revolution describes the angle of a circular surrounding sector as it rotates! This means one full revolution is 360 degrees. And half of a revolution is 180 degrees!
Last Spring, several of the Mt. Hood Community College (MHCC) jazz groups held a joint concert. Tickets sold for $8.00 to the general public and for $5.50 for students and staff. Ticket sales brought in $2,582.50. If 390 people attended the concert, how many were MHCC students and staff, and how many were general public? Using the variable p for the general public, and s for students/staff, write a system of equations to determine the breakdown of attendees.
The number of general public and students are 175 and 215 respectively.
How to calculate the value?Based on the information given:
Let p = general public
Let s = students/staff
390 people attended the concert. This will be:
p + s = 390 .... i
Tickets sold for $8.00 to the general public and for $5.50 for students and staff. Ticket sales brought in $2,582.50. This will be:
8p + 5.5s = 2582.5 .... ii
From equation i
p = 390 - s
8p + 5.5s = 2582.5 .... ii
8(390 - s) + 5.5s = 2582.5
3120 - 8s + 5.5s = 2582.5
Collect like terms
- 8s + 5.5s = 2582.5 - 3120
-2.5s = - 537.5
Divide
s = 537.5 / 2.5
s = 215
Students = 215
Note that p + s = 390
p + 215 = 390
P = 390 - 215
P = 175
Public = 175
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An investor invested a total of $2,900 in two mutual funds. One fund eamed a 7% profit while the other eamed a 3% profit. If the investor's total profit was $143, how much was invested in each mutual fund?
Answer:
one is 203
two is 87
Step-by-step explanation:
Find the slope of the line that passes through the pair of points.
(3, 1), (9, 1)
Answer:
gradient:
y2-y1/x2-x1
1-1/9-3
0/-6
= 0
Find the value of r so that the line passing through (-3, r) and (7,-6)
has a slope of 2 2/5
r =
The value of r is -10 for line with slope 2/5 .
What is slope?
A line's slope, often known as its gradient, is a numerical representation of the line's steepness and direction.
Main Body:
We know that the slope of line in two point form is
(y₂-y₁)/(x₂-x₁) = m where m = slope
given points are (-3,r) and (7,-6) m= 2/5
(-6-r)/(7+3)= 2/5
(-6-r)/10 =2/5
therefore value of r= -10
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in how many ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards? a) 120 b) 42,504 c) 5,100,480 d) 25 e) 4 f) none of the above.
In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.
Define combination.Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Given,
Ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards:
Through combination:
²⁴C₅
24!/51(24-5)!
Simplifying:
24!/5!(19!)
24 × 23× 22× 21× 20×19!/5! × 19!
24 × 23 × 22 × 21 × 20/ 5× 4 × 3 × 2 × 1
42504
In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.
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A tortoise and a hare run in the NYC marathon (26.2 miles). The hare crosses the finish line first in a time of 4 hours and 30 minutes. How fast did the hare run?
The hare ran 5.8 mph to win the race.
What is Speed?Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.
Given that, a tortoise and a hare run in the NYC marathon for 26.2 miles, the hare crosses the finish line first in a time of 4.5 hours.
Speed = distance/time
Speed of hare = 26.2/4.5 = 5.8 mph
Hence, The hare ran 5.8 mph to win the race.
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Find the value of (2.4) · (1.3). Show your reasoning.
The evaluation of the expression (2.4) · (1.3) gives 3.12
How to evaluate the expression?From the question, we have the following expression that can be used in our computation:
(2.4) · (1.3)
Express as products
This gives
(2.4) * (1.3)
Remove the brackets
So, we have the following representation
2.4 * 1.3
Evaluate the product
3.12
Hence, the solution is 3.12
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Which equation represents a line which is parallel to the y-axis?
A.x=−4y
B.x=−8
C.y=x−3
D.y=−7
An equation for a line that is parallel to the y - axis, based on the options, is B.x = −8.
How to know lines parallel to the y - axis?The y - axis is a vertical line which runs straight through the x - axis. This means that the coordinates of the y - axis are expressed in terms of 0. The y - axis intercepts the x - axis at point 0 which is why the coordinates are:
x = 0
Any line that is parallel to the y - axis will therefore be expressed in terms of x as well. The equation for a line that is parallel to the y - axis is therefore:
x = -8
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What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
See below
Step-by-step explanation:
Find slope using two convenient integer coordinates
(-1,4) and (1, -8) are convenient
slope = (y1-y2) / (x1-x2) = (4 - -8) / ( -1 -1) = 12/-2 = -6
the y-axis intercept is -2 ( by looking at the graph)
y = -6x -2 Done.
Find the perimeter of a rug that measures 2 yards by 11/12 yards
Answer:
5 5/6 yards
Step-by-step explanation:
You want the perimeter of a rug that is 2 yards by 11/12 yards.
PerimeterThe formula for the perimeter of a rectangle is ...
P = 2(L+W)
Using the given values, we find the perimeter to be ...
P = 2(2 yd + 11/12 yd) = 4 22/12 yd = 5 5/6 yd
The perimeter of the rug is 5 5/6 yards.
The temperature at the end of the day was 87 degrees. The temperature had decreased twice during the day, once by 9 degrees and another time by 7 degrees.
Which expression shows what the temperature was at the start of the day?
71+9+771+9+7
87−9−7
87+9+7
87+9−7
The temperature at the end of the day was 87 degrees. The temperature had decreased twice during the day, once by 9 degrees and another time by 7 degrees.
Which expression shows what the temperature was at the start of the day?
71+9+771+9+7
87−9−7
87+9+7
87+9−7
Approximately how many feet tall is the streetlight
Answer:
H = 30 ft
Step-by-step explanation:
Since the triangle is 90 degrees and we have to find out how tall the streetlight is we have to subtract 90 and 40 degrees. Which we get 50 degrees, after we subtract 20 from the 50 degrees. So we get 30 ft or 30 degrees.
What type of angles are labeled and what is the value of m? Show your work.
Answer:
see explanation
Step-by-step explanation:
m + 20 and 100 are vertically opposite angles and are congruent , then
m + 20 = 100 ( subtract 20 from both sides )
m = 80
The angles are vertically opposite angles and value of m is 80°
What is vertically opposite angles?Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
Given two angles which are Vertically opposite to each others,
We know Vertically opposite angles are equal to each other, so,
m + 20° = 100°
m = 100° - 20°
m = 80°
Hence, the value of m is 80°
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correct answer gets brainliest!
Answer:
arc RP = 136°
Step-by-step explanation:
the inscribed angle PQR is half the measure of its intercepted arc, then
arc PR = 2 × ∠ PQR = 2 × 68° = 136°
A men’s basketball coach would like to know if there is a relationship between how tall a player is and how high he can jump. Here is a scatterplot of the data.
A graph has height (inches) on the x-axis and vertical jump distance (inches) on the y-axis. The points form a line with positive slope.
Describe the scatterplot.
The relationship between height and vertical jump distance is
,
, and
.
There are
unusual observations.
The relationship between height and vertical jump is High positive correlation.
What is a correlation?
A statistical indicator of the relationship between the relative motions of two variables is the correlation. If the variables are correlated, a line or curve will be formed by the points. The points will touch the line more closely the better the correlation.
Main body:
To find the relation we need to draw a line passing closely to all the points , if we are able to draw such line , it has high positive correlation.
If the line doesn't pass through all points it has low positive correlation.
hence this has high positive correlation .
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Answer:
-positive
-linear
-strong
-no.
Step-by-step explanation:
edge 2023
Solve for v in terms of u and w.
u= –vw
Which expression is the factored form of−4.5n+3?
Responses
A. −3(1.5n−1)
B. −1.5(3n+2)
C. −1.5(−3n+2)
D. −3(1.5n+1)
An expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)
The correct answer is an option (A)
In this question we have been given an expression -4.5n + 3
We need to identify an expression which is factored form of given expression.
If we simplify the factored form then it must be a give expression.
consider ,A. −3(1.5n−1)
= -4.5n + 3
consider an expression B. −1.5(3n+2)
= -4.5n - 3
consider C. −1.5(−3n+2)
= 4.5n - 3
consider D. −3(1.5n+1)
= -4.5n - 3
Therefore, an expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)
The correct answer is an option (A)
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What is the least angle measure by which this figure can be
rotated so
that it maps onto itself?
45°
90°
180°
360°
90° is the least angle measure by which this figure can be rotated so that it maps onto itself.
The correct option is (B)
From the figure,
As the figure has two axis of symmetry, placing x and y axis such that the origin lies on its centroid.
Angle between x axis and y axis is 90°.
So rotating any degree which is a multiple of 90 i.e., 90°, 180°, 270°, 360°...… would yield the original figure.
Therefore, 90° is the least angle measure by which this figure can be rotated so that it maps onto itself.
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Solve for the value of e.
Answer: e=
(9e-8)
(4e+6)
Submit Answer
posse
Answer:
Step-by-step explanation:
Expand: 36e^2+12e-48=e
Subtract e from both sides 36e^2+11e-48=0
Using the quadratic formula, e=(-11+-sqrt7033)/72
If one factor of -24x^4y^5+16x^2y^3 is -8x^2y^3 what is the other factor
The polynomial is, -24x⁴y⁵+16x²y³. One of the factor is (-8x²y³),So other factor is 3x²y²-2 by the factorization method.
What is polynomial?Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The terms degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Here,
The polynomial is,
=-24x⁴y⁵+16x²y³
One of the factor is (-8x²y³)
=-8x²y³*(3x²y²-2)
So other factor is 3x²y²-2.
One of the factor is (-8x²y³),So other factor is 3x²y²-2 by the factorization method for the The polynomial -24x⁴y⁵+16x²y³.
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Solve the equation given a domain of {-3}.
3x - 2y = 5
The solution to the equations is y = -7
How to solve the equations using the domain of the replacement sets?From the question, we have the equation to be given as
3x - 2y = 5
The above equation is a linear equation
The domain or the replacement set is given as
{-3}
Rewrite properly as
Domain = {-3}
or
x = -3
So, we replace the variables using the elements in the replacement set
When x = -3, we have
3 x -3 - 2y = 5
Evaluate the products
This gives
-9 - 2y = 5
Add 9 to both sides
-2y = 14
Divide both sides by -2
y = -7
So, we have
x = -3 and y = -7
Hence, the solution to the equation is y = -7
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