in the athletics team, tall members tend to win three times as many medals as short members.20 number of medals have been won by short athletes.
This question can be solved by using the ratio method. Since tall athletes are said to win three times as many medals as short athletes, this means that the ratio of tall athletes' medals to short athletes' medals is 3:1. We can use this ratio to calculate how many medals have been won by short athletes. Since the team has won a total of 60 medals, we can divide this number by 4 (the total number of medals in the ratio) to get 15. We then multiply 15 by the ratio of short athletes' medals (1) to get 15 medals. This means that short athletes have won 20 medals, since 15 multiplied by 3 is 45, leaving 60-45=15 medals for the short athletes. Thus, 20 medals have been won by short athletes.
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Two friends visited a taffy shop. Winston bought 2 kilograms of strawberry taffy and 1 kilogram of banana taffy for $20. Next, Audrey bought 4 kilograms of strawberry taffy and 4 kilograms of banana taffy for $52. How much does the candy cost?
The costs for the given candy are $7 for strawberry taffy and $6 for banana taffy. By writing equations and simplifying them, we get the requiredd values.
How to solve two equations?To solve two equations,
Rewrite one of the equations for one of its variables.Substitute it in the other equation.On simplifying, we get a value for one variable.Then, substitute in one of the equations, and we get another variable.This method of solving is called the substitution method.Calculation:It is given that, two friends visited a taffy shop.
Winton bought - 2 kg of strawberry taffy and 1 kg of banana taffy for $20.
Audrey bought - 4 kg of strawberry taffy and 4 kg of banana taffy for $52.
Then, we can write the above information into equations as
2S + B = 20 ...(1)
4S + 4B = 52 ...(2)
Where S represents strawberry taffy and B represents banana taffy.
From (1), we can write
B = 20 - 2S
Then, on substituting in (2), we get
4S + 4(20 - 2S) = 52
⇒ 4S + 80 - 8S = 52
⇒ -4S = 52 - 80 = -28
⇒ 4S = 28
∴ S = 7
Thus, the cost of strawberry taffy is $7.
On substituting S = 7 in (1), we get
2(7) + B = 20
⇒ 14 + B = 20
⇒ B = 20 - 14
∴ B = 6
Thus, the cost of banana taffy is $6.
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Find the volume of this prymaid in question 10.
PLEASE HELP ME.
Answer:
5.083
Step-by-step explanation:
[tex]V=\frac{1}{3}Bh=(1/3)(1/2)(1.7)(3.9)(4.6)=5.083[/tex]
Julius went fishing on Saturday morning. He took a cooler to store the fish that he caught. The cooler could hold less than 8 large fish. Write an inequality that represents how many fish the cooler could hold.
8 > f
8 < f
8 ≥ f
8 ≤ f
Answer:
8 < f
Step-by-step explanation:
Because it says the cooler could hold less than eight large fish
Less than mean <
So the equation is 8<f
Answer: b 8 < f
Step-by-step explanation:
Mr. Harold invested $1,600 in an account
that paid him 3.25% simple interest. What
will be the balance of his account after
32 years, including interest?
A) $1,664.00
C) $16,640.00
B) $1,536.00
D) $3,264.00
Answer:
D) $3,264.00
Step-by-step explanation:
I = Prt
I = $1600 × 0.0325 × 32 = $1664
total = $1600 + $1664 = $3264
How many times smaller is 1.2 × 106 than 1.35 × 107?
11.25
2.55
1.47
0.15
Answer:
11.25
Step-by-step explanation:
(1.35 × 10^7) / (1.2 × 10^6) =
= 135/12
= 11.25
Answer: 11.25 is the answer
You wish to purchase a 14 pound bag of mixed nuts. Peanuts are $5.00 per pound and almonds are $6.00 per pound. How many pounds of peanuts should you buy if the entire bag costs $74.
[Please show and explain how you solved this word problem.]
Answer:
10 pounds
Step-by-step explanation:
You want to know the number of pounds of peanuts in a mix of $5/lb peanuts and $6/lb almonds that gives 14 pounds of nuts for $74.
SetupLet p represent the number of pounds of peanuts in the mix. The (14-p) is weight of almonds, and the total cost is ...
5p +6(14 -p) = 74
SolutionSimplifying the equation gives ...
-p +84 = 74
10 = p . . . . . . . . add p-74
You should buy 10 pounds of peanuts to make the 14 lb bag cost $74.
__
Additional comment
You notice that simplifying the equation gives p a negative coefficient. If you choose the variable to represent the more expensive contributor, then the coefficient of that comes out positive. (We like positive coefficients, as they tend to reduce errors.)
Here, the problem is requesting the amount of the lower cost contributor, so we used the variable to represent that.
Often, you are asked to solve mixture problems using a system of equations. Those would use a variable for each of the quantities, and the equations would be ...
p + a = 14 . . . . . . . total weight5p +6a = 74 . . . . . total costYou notice that substituting for 'a' gives the equation we used above.
a = 14 -p . . . . . . . . . . . . . write an expression for 'a'5p +6(14 -p) = 74 . . . . . use the expression for 'a'Jumping directly to this step saves a bit of written work, though the mental work is the same.
Which inequality is represented by this graph?
The linear equality for the given graph is x > 0.
Option (B) is correct.
What is linear equality?
In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
The hollow circle in the linear equality shows that the point should be excluded and the line is going towards the positive x-axis.
So we can prepare the linear equality as
x > 0
Hence, the linear equality for the given graph is x > 0.
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please help me im not very smarts
Answer:
1,5,7 = 145 degrees
2,3,6,8 = 35 degrees
Step-by-step explanation:
1,5, and 7 are interior angles:
Interior angles are those that lie inside a polygon. For example, a triangle has 3 interior angles. The other way to define interior angles is "angles enclosed in the interior region of two parallel lines when intersected by a transversal are known as interior angles".
2,3,6, and 8 are exterior angles:
An Exterior Angle is the angle formed by one side of a polygon and the extension of the adjacent side. In all polygons, there are two sets of exterior angles, one that goes around clockwise and the other goes around counterclockwise.
Hope this helps :))
Noah thinks the answers to these two questions will be the same.
Do you agree with him? Explain your reasoning.
◦ This year, a herd of bison had a 10% increase in population. If there were 550 bison in the herd last year, how many are in the herd this year?
◦ This year, another herd of bison had a 10% decrease in population. If there are 550 bison in the herd this year, how many bison were there last year?
Answer: No, it works out to a different number. The 1st will end up with 605 bison.
Step-by-step explanation:
1st Herd: (550 x 10%) = 55 Bison
550 + 55 = 605 Thus 550 with a 10% increase is 605 Bison.
2nd herd: if you take 10% of 605 bison that number of (60.5) will give you a greater loss when taken away from 605.
605 - 60.5 = 544.5 bison remaining if 605 has a 10% loss.
Herd 2 started with approximately 611 bison. Check your math by multiplying 611 by 10% = 61.1
then subtract (611 - 61.1) = 549.9
So Herd 1 Does Not Equal Herd 2.
pls tell me the qanswer da
Answer: B
Step-by-step explanation:
Answer:
it's point B
Step-by-step explanation:
The difference between -4 and -2 is -2 . And there are 8 steps from -2 and to -4.This means each step represents -2/8 which equals to -1/4. Then divide that number by -1/4
[tex] -2 \frac{6}{8} \div \frac{1}{4} \\ = 11[/tex]
Then count 11 steps from 0
ok.
when a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be
when a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be norm-referenced.
Norm-referenced tests are assessments that measure an individual's performance against a predetermined group, or norm. A norm-referenced test is designed to evaluate how a person performs in comparison to a representative and pretested sample of people. This type of testing is especially common with achievement tests, such as the SAT or IQ tests, where the scores are meant to represent how the individual compares to others of the same age or in the same educational setting. The results of norm-referenced tests can be used to rank individuals according to their performance on the test, allowing for an easy comparison between individuals. Norm-referenced tests are designed to provide a comprehensive view of an individual’s strengths and weaknesses in comparison to a predetermined group.
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or One angle of a triangle measures 70°. The other two angles are in a ratio of 3:8. What are the measures of those two angles?
Answer: The answer would be 9.125.
Step-by-step explanation:
I can't really find an explanation for it. Sorry.
The remaining angles are 80 and 30
The sum of angles of a triangle = 180
One angle is given as = 70
The sum of the remaining angles= 110
Now we apply the theory of ratios
The ratio between the angles are given as 3:8
So one angle will be 3 parts of 110 and other eight parts of 110
Total number of parts = 3+8 = 11
Angle 1 = (3*110)/11
= 30
Angle 2 = (8*110)/11
= 80
So the other two angles are 30 and 70.
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Melissa made three batches of oatmeal cookies. Her recipe calls for amounts of sugar (in cups) and flour (in cups) in the following ratios. What is the unit rate of change of flour (y) to respect sugar (x)? That is, how much flour corresponds to one cup of sugar? The unit rate of change is 2.25. How do I graph this?
The unit rate of change of flour (y) with respect to sugar (x) will be 2.25.
What does the unit rate of change means?The unit rate of change means by how much times a specific quantity changes per unit change in other quantity. For a function, y = f(x), the unit rate of change is given by -r = Δy/Δx
[tex]\lim_{x \to \;0} (r) = \lim_{x \to \;0}[/tex] (Δy/Δx) = dy/dx
Given is that Melissa made three batches of oatmeal cookies. Her recipe calls for amounts of sugar (in cups) and flour (in cups) in the following ratios as shown in the question.
We can write the rate of change as -
r = Δy/Δx
r = (y₂ - y₁)/(x₂ - x₁)
y₂ = [tex]$6\frac{3}{4}[/tex] = 27/4
y₁ = [tex]$4\frac{1}{2}[/tex] = 9/2
x₂ = 3
x₁ = 2
Using the values -
r = (27/4 - 9/2)/(3 - 2)
r = (27 - 18)/4
r = 9/4
r = 2.25
Therefore, the unit rate of change will be 2.25.
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The length, L, of a teel rod i 7. 36, correct to 2 decimal place. Complete the error interval for length L
The length, L, of a teel rod i 7. 36, correct to 2 decimal place then The error interval for L is [7.355,7.365)
we know that
In this problem
The least significant digit is in the hundredths place.
The error can be as much 0.005 m
Determine the lower bound
To find out the lower bound subtract the error from the value
so 7.355
Determine the upper bound
To find out the upper bound adds the error to the value
7.365
so
Since 7.365 is rounded up to 7.37, the maximum value of L must be less than that.
therefore
7.355 < L < 7.365
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Find the volume of the largest right circular cone that can fit in a cube whose
edge (height) is 14cm.
The largest right circular cone that can fit within a cube has a volume of 718.67 cm3.
Explain about the circular cone?When a cone's axis is the line from the vertex to the circular base's midpoint, the cone is said to be right circular. In other words, a right angle is formed when the center of the circular base joins the cone's peak.
A three-dimensional form called an inverted frustum that resembles a conical cylinder. When the vertex of a cone is inverted after being sliced by a plane parallel to the shape's base, it is said to have this shape.
The formula r2+rl, where r is the radius of the circular base, h is the height of the cone, l is the slant height, and is an approximation, is used to determine the surface area of a cone as 3.14
Side of cube: 14 cm
Cube's radius is 14/2 cm, or 7 cm.
h=14cm for height
Volume'=1/3piR x 2hM =1/3 x 22 x 7 x 7 x7
= 718.67 cm3.
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show the work to prove that the series is convergent using one of the convergence series tests. b. what does the divergence test say and why does the divergence test fail for this series?
the work to prove that the series is convergent using one of the convergence series tests.the series a is convergent and series b is divergent.
a. The alternating series test can be used to prove that the series is convergent. The alternating series test states that if a series is of the form [tex]$a_1-a_2+a_3-a_4+\cdots$[/tex] and satisfies the conditions:
1. [tex]$a_n \geq 0$[/tex] for all n
2. [tex]$a_{n+1} \leq a_n$[/tex] for all n
3. [tex]$\lim_{n\to \infty} a_n = 0$[/tex]
Then the series is convergent.
In this case, the series is of the form [tex]$2-\frac{2}{2}+\frac{2}{3}-\frac{2}{4}+\cdots$[/tex] which satisfies all the conditions of the alternating series test.
Therefore, the series is convergent.
b. The divergence test states that if the limit of the sequence of partial sums is not finite, then the series is divergent. However, in this case, the limit of the sequence of partial sums is finite and thus the divergence test fails to prove that the series is divergent.
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5
X
+
X+5
3x 1
#5 is the one I need solved please.
Answer:
x = 11midline = 16baseline = 32Step-by-step explanation:
You have a triangle with its midline length given as x+5 and its parallel base line length given as 3x-1. We presume you want to know the value of x and the lengths of the segments.
MidlineThe midline is half the length of the parallel base line, so you have ...
x +5 = 1/2(3x -1)
Solution2x +10 = 3x -1 . . . . . . . multiply by 2
11 = x . . . . . . . . . . . . . add 1-2x
The midline length is x+5 = 11+5 = 16.
The base line length is 3x-1 = 33 -1 = 32, twice the length of the midline.
The solution to the triangle is ...
x = 11midline = 16base line = 32please help!.....Answer the questions about the following polynomial.
Answer:
The expression represents a cubic polynomial with 3 terms. The constant term is -1, the leading term is x^3, and the leading coefficient is 1.
Step-by-step explanation:
if the coefficient of determination is a positive value, then the regression equation
Answer:
close to 1, good fit
Step-by-step explanation:
If the coefficient of determination is a positive value, it means that the regression equation is a good fit for the data. The coefficient of determination, denoted by r^2, is a measure of how well the regression equation explains the variation in the data. A value of r^2 close to 1 indicates that the regression equation explains a large portion of the variation in the data, while a value of r^2 close to 0 indicates that the regression equation does not explain much of the variation in the data.
Therefore, if the coefficient of determination is a positive value, it means that the regression equation is a good fit for the data and explains a significant portion of the variation in the data. This means that the regression equation is likely to be a reliable model for the data and can be used to make predictions about the values of the dependent variable based on the values of the independent variable.
Choose the equation of a line parallel to the given equation and passing through a point P. -3x - y= -4 ; P = (1,4)
A.) Y = 1/3x + 7
B.) Y = -3x + 7
C.) Y = -3x +5
D.) Y = 1/3x -3
The equation of a line parallel to -3x - y= -4 and passing through a point (1,4) is y = -3x + 7.
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line is parallel to -3x - y = -4 and it passes through (1, 4).
Parallel lines have the same slope.
Hence,
-3x - y = -4
y = -3x + 4
The slope of the line is -3.
Let's find y-intercept using (1, 4)
y = -3x + b
4 = -3(1) + b
4 + 3 = b
b = 7
Therefore, the equation of the line is y = -3x + 7.
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Given the inequality 3(n − 6) < 2(n + 12), determine which integer makes the inequality false.
S:{−5}
S:{3}
S:{12}
S:{42}
The integer that makes the inequality 3(n − 6) < 2(n + 12) false is
S:{42}How to find the integer that makes the inequality falseThe integer that makes the inequality false is solved by substituting the values and solving the inequality
3(n − 6) < 2(n + 12)
for n = -5
substituting the value of n
3(-5 − 6) < 2(-5 + 12)
= -33 < 14
3(n − 6) < 2(n + 12)
for n = 3
substituting the value of n
3(3 − 6) < 2(3 + 12)
= -9 < 30
3(n − 6) < 2(n + 12)
for n = 12
substituting the value of n
3(12 − 6) < 2(12 + 12)
= 18 < 48
3(n − 6) < 2(n + 12)
for n = 42
substituting the value of n
3(42 − 6) < 2(42 + 12)
= 108 < 108 wrong
This is the only wrong solution since 108 = 108
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What is the value of (−135) − 72 − (−16)?
−47
−79
−191
−223
Answer:
-191
Step-by-step explanation:
Answer:
[tex] \sf \: c) - 191[/tex]
Step-by-step explanation:
Given problem,
→ (-135) - 72 - (-16)
Let's solve the problem,
→ (-135) - 72 - (-16)
→ (-135) - 72 + 16
→ (-135 - 72) + 16
→ -(135 + 72) + 16
→ -207 + 16
→ -191
Hence, answer is -191.
Eliminate the y in the following system of equations. What is the result when you add the two equations?
x+y=2
3x-4y=27
Answer:
thus: x = 5, y = -3
Step-by-step explanation:
Solve the following system:
{y + x = 2 | (equation 1)
-4 y + 3 x = 27 | (equation 2)
Swap equation 1 with equation 2:
{3 x - 4 y = 27 | (equation 1)
x + y = 2 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{3 x - 4 y = 27 | (equation 1)
0 x + (7 y)/3 = -7 | (equation 2)
Multiply equation 2 by 3/7:
{3 x - 4 y = 27 | (equation 1)
0 x + y = -3 | (equation 2)
Add 4 × (equation 2) to equation 1:
{3 x + 0 y = 15 | (equation 1)
0 x + y = -3 | (equation 2)
Divide equation 1 by 3:
{x + 0 y = 5 | (equation 1)
0 x + y = -3 | (equation 2)
Collect results:
Answer: {x = 5, y = -3
Directions: Evaluate the following logarithmic functions.
1. log100.1
2. log5125
3. log864
4. log1/3 9
5. log1/21/2
6. log497
7. log9 3
8. log3 81
9. log4 8
10. log100 10,000
The result of the logarithmic functions by logarithm tables are listed below:
- 232- 211 / 21 / 243 / 22How to evaluate logarithmic functions
This question can be resolved by means of logarithm properties and logarithm tables or numerical methods. Now we proceed to evaluate each logarithmic functions:
Case 1:
㏒₁₀ 0.1
By using rational numbers:
㏒₁₀ (1 / 100)
By logarithm properties:
㏒₁₀ 1 - ㏒₁₀ 100
By logarithm tables:
0 - 2
- 2
Case 2:
㏒₅ 125
By logarithm tables:
3
Case 3:
㏒₈ 64
By logarithm tables:
2
Case 4:
[tex]\log_{\frac{1}{3} } 9[/tex]
By logarithm tables:
- 2
Case 5:
[tex]\log_{\frac{1}{2}} \frac{1}{2}[/tex]
By logarithm tables:
1
Case 6:
㏒₄₉ 7
By logarithm tables:
1 / 2
Case 7:
㏒₉ 3
By logarithm tables:
1 / 2
Case 8:
㏒₃ 81
By logarithm tables:
4
Case 9:
㏒₄ 8
By logarithm tables:
3 / 2
Case 10:
㏒₁₀₀ 10,000
By logarithm tables:
2
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Let X = {x|x is a whole number less than 10} and Y= {-3, -2, 1, 3, 5, 7, 20}. Find X n Y.
3
21
The values of X ∩ Y are 1, 3, 5, and 7.
What is a set?A set is a collection of items where there are operations such as:
Union of sets, the intersection of sets, complements of sets.
We have,
X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
Y = {-3, -1, 1, 3, 5, 7, 20}
Now,
X ∩ Y
= The values common to both sets.
= {1, 3, 5, 7 }
Thus,
X ∩ Y = {1, 3, 5, 7 }
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suppose y′=f(x,y)=xycos(x)y′=f(x,y)=xycos(x).
The partial derivative of function f(x, y) = xy/cos(x) is ∂/∂y [xy/cos(x)] = x sec(x)
In this question we have been given a function y′ = f(x,y) = xy/cos(x)
We need to find the partial derivative of function f(x, y) with respect to y, ∂f/∂y
Consider the partial derivative of function
∂f/∂y = ∂/∂y [xy/cos(x)]
∂f/∂y = ∂/∂y [xy * 1/cos(x)]
we know that 1/cos(x) = sec(x)
∂f/∂y = ∂/∂y [xy * sec(x)]
∂f/∂y = x sec(x) ∂/∂y (y)
∂f/∂y = x sec(x) * 1
∂f/∂y = x sec(x)
Therefore, ∂/∂y [xy/cos(x)] = x sec(x)
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Find the measure of <1
A. 145 degree
B. 36 degree
C. 109 degree
D. 35 degree
Please help!!!
Picture is provided
Answer:
A. 145 degree
Step-by-step explanation:
A triangle has 180 degree
109 + 36 = 145 degree
180 - 145 = 35 degree
35 degrees is the missing angle of the triangle. This angle must add with angle 1 equal to 180 degrees.
180 - 35 = 145 degree
So, the answer is A
Answer:
ANGLE 1 = 145°
Step-by-step explanation:
Angle 1 is right next to the EMPTY interior angle of the triangle and they are on a straight line!
This means, these two angles (angle 1 and the empty angle next to it) are supplementary angles!
Supplementary angles are angles on a straight line and they always add up to 180°
To find it, we need to find the degrees of the empty angle.
To find it, we need to look at the whole triangle.
Remember, all triangles equal 180°
Let's find this empty angle
180° - 109 - 36 = 35°
The empty angle = 35°
BUT WE ARE NOT DONE!
We are looking for angle 1, not the empty angle.
To find angle 1, we must remember that the empty angle (which we found was 35°) and angle 1 make a supplementary angle (which totals up to 180°)
Let's find angle 1, using subtraction.
180° - 35 = 145°
ANGLE 1 = 145°
As a pharmacist, you are responsible for knowing about medication dosage, and how long a dose stays in the patient's system. Let's look at an example of a common medication, called ibuprofen. When a patient takes a 400 mg dose of ibuprofen, it releases into the bloodstream at a certain rate, and then decreases over time. The function that models this concentration of medicine over time is complex and looks like this:
P(t) = 0.5t + 3.45t³ - 96.65t² + 347.7t, when 0 ≤t≤6 . In this function above, P(t) is the amount of medication (in mg) in the
blood stream at time t (in hours).
When put into a graphing software, it looks like this:
1) Why do we only need to look at the interval 0 ≤ t ≤ 6
The effect of the medicine is only left for the interval of 0 ≤ t ≤ 6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Let's look at an example of a common medication, called ibuprofen. When a patient takes a 400 mg dose of ibuprofen, it releases into the bloodstream at a certain rate and then decreases over time. The function that models this concentration of medicine over time is complex and looks like this:
P(t) = 0.5t + 3.45t³ - 96.65t² + 347.7t, when 0 ≤t≤6.
The graph is repeating after the value of t as 6.
Hence, the interval will be 0 ≤t≤6.
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This data records the ages of people on a bus to the seaside.
2 4 25 31 3 23 24 26 37 42
60 76 33 24 25 18 20 77 5 13
18 13 15 49 70 48 27 25 24 29
Find the median age, making your method clear.
Answer:
The median is 25
Step-by-step explanation:
I counted the numbers and it was 30 I divided it to 2
1/6+5.4 as a fraction in simpelest form
Answer: 167/30
Step-by-step explanation:
1/6 + 5.4
5.4 = 54/10
So we have 1/6 + 54/10
The common factor is 60
10/60 + 324/60
334/60
167/30
Answer:
1/6 + 5.4 = 167/30 = 5 17/30
Step-by-step explanation:
Conversion of a decimal number to a fraction: 5.4 = 54/
10
= 27/5
a) Write down the decimal 5.4 divided by 1: 5.4 = 5.4/
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
5.4/1
= 54/10
Note: 54/10
is called a decimal fraction.
c) Simplify and reduce the fraction
54/10
= 27 * 2/5 * 2
= 27 * 2/5 * 2 = 27/5
Add: 1/6 + 5.4 = 1/6 + 27/5 = 1 · 5/
6 · 5 + 27 · 6/
5 · 6
= 5/30 + 162/30 = 5 + 162/30
= 167/30