Answer:
The interest is
$ 769.50Step-by-step explanation:
Simple interest is given by
[tex]I = \frac{P \times R \times T}{100} [/tex]
where
P is the principal
R is the rate
T is the time given
From the question
The principal / P = $ 5700
The rate / R = 4.5%
The time given / T = 3 years
So the interest is
[tex]I = \frac{5700 \times 4.5 \times 3}{100} [/tex]
[tex]I = \frac{76950}{100} [/tex]
We have the final answer as
I = $ 769.50
Hope this helps you
6th grade math, help me please
Answer:
1. 2/5
Step-by-step explanation:
When it says the ratio is 5 to 2, that means 5 is always first:
5 : 2 is correct
5/2 is correct
10 : 4 is correct (multiplied 2 on both sides)
2/5 is incorrect because 2 is first. That means that this ratio would be 2 to 5, not 5 to 2.
Answer:
2/5
Step-by-step explanation:
because you are not supposed to flip the two numbers. You need to keep them in the same order.
Sorry, if this isn't the greatest answer. Its my first time.
According to medical data, the ages at which patients have their first knee replacement surgery
follows a normal distribution. The average age for a first knee replacement is 58 years of age, with a
standard deviation of 8.25 years. Therefore, doctors can expect the middle 68% of their knee
replacement surgery patients to be between what ages?
Answer:
The doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.
Step-by-step explanation:
68 % of the knee replacement surgery patients implies that the ages lies within x = x₀ ± σ where x₀ = mean age = 58 years and σ = standard deviation = 8.25 years
So, the ages lies between x₀ + σ and x₀ - σ
So, the ages lie between 58 - 8.25 = 49.75 years
and 58 + 8.25 = 66.25 years
So the doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.
4. Simplify the following.
3
a. 2-X5-:11
3
x5
5
6
7
Answer:
[tex]1 \frac{1}{4} [/tex]Step-by-step explanation:
[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]
Convert the mixed number to an improper fraction
[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]
To divide by a fraction, multiply the reciprocal of that fraction
[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]
Reduce the number with the G.C.F 7
[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]
Reduce the numbers with the G.C.F 17
[tex] \frac{5}{6} \times \frac{3}{2} [/tex]
Reduce the numbers with the G.C.F 3
[tex] \frac{5}{2} \times \frac{1}{2} [/tex]
Multiply the fraction
[tex] \frac{5}{4} [/tex]
In mixed fraction:
[tex]1 \frac{1}{4} [/tex]
Hope this helps..
Good luck on your assignment...
Examine today’s stock listing for SFT Legal, shown below. 52 wk High 52 wk Low Symbol Div. Close Net Change 74.80 44.61 SFT 8.94 56.11 5.74 What was the price of SFT Legal yesterday? a. $47.17 b. $56.11 c. $50.37 d. $61.85
Answer:
c. $50.37
Step-by-step explanation:
Close price was $56.11 and net change was $5.74. so subtract the net change from the close to get yesterday's price.
Answer:
c.50.37
Step-by-step explanation:
Does this graph show a function? Explain how you know.
O A. No; there are yvalues that have more than one x-value.
ОО
B. Yes; there are no y-values that have more than one x-value.
C. No; the graph fails the vertical line test.
ОО
D. Yes; the graph passes the vertical line test.
It is possible to draw a single straight line to pass through more than one point on the red curve. Therefore, the graph fails the vertical line test. We have cases where one input leads to more than one output.
Aiden is trying to pick up some lawn mowing jobs over the weekend to make extra money for a school trip. Each lawn in his neighborhood takes an average of 40 minutes to mow, and Aiden has no more than 11 hours, or 660 minutes, of available time to mow lawns. If Aiden mows his grandparents' farm which takes him 110 minutes, and x represents the number of lawns he mows in his neighborhood, which inequality represents this situation?
A.
40x + 110 ≤ 660
B.
110x + 40 ≤ 660
C.
110x + 40 ≥ 660
D.
40x + 110 ≥ 660
Answer:
A.
Step-by-step explanation:
40x is the number of lawns he can do, less the time to do his grandparents time (added to other law time) and he has 660 mins of less to complete them.
Answer:
a. 40x + 110 ≤ 660
Step-by-step explanation:
The graph for the equation y=-2x+1 is shown below.
ch
-3
-2 -2
х
-2
-3
If another equation is graphed so that the system has no solution, which equation could that be?
O y=-2(x-3)
Hark this and return
Save and Exit
Next
Submit
Answer:
Step-by-step explanation:
Given the equation y=-2x+1 and given another equation y=mx+b in order for us to have no solution we must guarantee that both lines do not intersect. Recall that m is the slope of the second equation and b the y-intercept. To guarantee that both lines don't intersect, they must be parallel. To have this result, we must have that they have the same slope but different y intercept. That is take m = -2 and b any value different to +1. For example, the b = 6. So
y = -2x+6 = -2(x-3) is another equation that gives no solution to the system.
Answer:
B. y = -1/2 (4x + 2)
Step-by-step explanation:
hope this is the answer that you are looking for :)
Factor d^2-10d+10 by grouping
Answer:
(d-5-√15)(d-5+√15)
Step-by-step explanation:
The average flight time from Seattle (SEA) to New York (JFK) is 4.3 hours. The distance between them is 2421 miles. The average flight time going the other way, JFK to SEA is 5.5 hours. The difference is due to the jet stream. Translate this situation to a system of equations and find the average speed of the jet and the average speed of the jet stream.
Answer:
Speed of the jet is 563.02 miles/hr
Speed of the jet stream is 122.83 miles/hr
Step-by-step explanation:
The average time for going from Seattle to New York is 4.3 hours
The distance between these places is 2421 miles
The average time for going back (impaired by jet stream) is 5.5 hours
If we designate the speed of the jet = v
and the speed of the jet stream = u
then on the return trip, the relative speed of the jet = v - u
Also, recall that distance = speed x time
For the going trip, the distance covered by the jet = 4.3 x v = 2421 miles
For the return trip, the distance covered by the jet = 5.5 x (v - u) = 2421 miles
= 5.5(v - u)
these translate into the following equation written below
4.3v = 2421 ....equation 1
5.5(v - u) = 2421 ....equation 2
solving, equation 1, we'll have
4.3v = 2421
v = 2421/4.3 = 563.02 miles/hr this is the speed of the jet
substituting the value of v into equation 2, we'll have
5.5(v - u) = 2421
5.5(563.02 - u) = 2421
3096.61 - 5.5u = 2421
3096.61 - 2421 = 5.5u
675.61 = 5.5u
u = 675.61/5.5
u = 122.83 miles/hr this is the speed of the jet stream
Can someone Give me the answer?
Answer:
(0,5)
Step-by-step explanation:
The solution to the system is where the two graphs intersect
From the graph, the graphs intersect at x = 0 and y =5
Step-by-step explanation:
I have trouble with these types of questions as well, but hopefully this might help.
The Stanford-Binet Intelligence Scale is an intelligence test, which, like many other IQ tests, is standardized in order to have a normal distribution with a mean of 100 and a standard deviation of 15 points.
As an early intervention effort, a school psychologist wants to estimate the average score on the Stanford-Binet Intelligence Scale for all students with a specific type of learning disorder using a simple random sample of 16 students with the disorder. Determine the margin of error, m, of a 99% confidence interval for the mean IQ score of all students with the disorder. Assume that the standard deviation IQ score among the population of all students with the disorder is the same as the standard deviation of IQ score for the general population, sigma = 15 points.
Answer:
The margin of error is [tex]MOE = 9.68[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n= 16[/tex]
The standard deviation is [tex]\sigma = 15[/tex]
The confidence level is [tex]C = 99[/tex]%
Generally the level of significance is mathematically evaluated as
[tex]\alpha = 100 - C[/tex]
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1%[/tex]%
[tex]\alpha = 0.01[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
The reason obtaining the critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because we are considering the two tails of the area normal distribution curve which is not inside the 99% confidence interval
Now the margin of error is evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 2.58 * \frac{15}{\sqrt{16} }[/tex]
[tex]MOE = 9.68[/tex]
Helpppp asapppppp....
Answer:
C.
Step-by-step explanation:
So, here's what you need to remember:
If we have a function f(x) and a factor k:
k(f(x)) will be a vertical stretch if k is greater than 1, and a vertical compression if k is greater than zero but less than 1.
f(kx) will be a horizontal compression if k is greater than 1, and a horizontal stretch if k is greater than zero but less than 1.
We are multiplying 0.5 to the function. In other words: 0.5f(x).
This is outside the function, so it's vertical.
0.5 is less than 1, so this would be a vertical compression
A large study of over 2000 parents and children in Norway found that toddlers who regularly slept less than 10 hours per night or woke frequently (three or more times) at night tended to experience more emotional and behavioral problems when they reached age five. The study involved a large random sample of mothers and children and was conducted over several years. What is the population of interest in this survey
Answer: Parents and children ( till the age of 5) of Norway
Step-by-step explanation:
The population in a survey is the group of people sharing common features or characteristics as per the researcher point of view.Here, A large study of over 2000 parents and children in Norway found that toddlers who regularly slept less than 10 hours per night or woke frequently (three or more times) at night tended to experience more emotional and behavioral problems when they reached age five.
Since the study involved a large random sample of mothers and children and was conducted over several years.
So, the population of interest in this survey is "Parents and children ( till the age of 5) of Norway".
In a class full of men and women, 5 9 of the class are women. What is the ratio of men to women in its simplest form?
Find the left critical value for 95% confidence interval for σ with n = 41. 26.509 24.433 55.758 59.342
Answer: 59.342
Step-by-step explanation:
The chi-square critical values are used to find the confidence interval for σ.
Left critical value = [tex]\chi^2_{\alpha/2, n-1}[/tex] [i.e. chi-square value from chi-square table corresponding to degree of freedom n-1 and significance level of [tex]\alpha/2[/tex]]
To find : left critical value for 95% confidence interval for σ with n = 41.
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
degree of freedom = 41-1=40
Now, the left critical value for 95% confidence interval for σ with n = 41 is the chi-square value corresponding to degree of freedom n-1 and [tex]\alpha/2=0.025[/tex]
=59.342 [from chi-square table ]
A catering company is catering a large wedding reception. The host of the reception has
asked the company to spend a total of $454 on two types of meat: chicken and beef. The
chicken costs $5 per pound, and the beef costs $ 7 per pound. If the catering company
buys 25 pounds of chicken, how many pounds of beef can they buy?
The answer is 47 pounds
Explanation:
1. First, let's calculate the amount of money that was spent on chicken
$5 per pound of chicken x 25 pounds = $125
2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.
$454 (total) - $125 (chicken) = $329
3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.
$329 / $7 = 47 pounds
Solve 2x2 – 6x + 10 = 0 by completing the square.
Answer: x = 6.32 or -0.32
Step-by-step explanation:
2x² - 6x + 10 = 0
No we divide the expression by 2 to make the coefficient of x² equals 1
We now have
x² - 3x + 5 = 0
Now we remove 5 to the other side of the equation
x² - 3x = -5
we add to both side square of half the coefficient of x which is 3
x² - 3x + ( ⁻³/₂)² = -5 + (⁻³/₂)²
(x - ³/₂)² = -5 + ⁹/₄
Resolve into fraction
(x - ³/₂)² = ⁻¹¹/4
Take the roots of the equation
x - ³/₂ = √¹¹/₄
x - ³/₂ = √11/₂
x = ³/₂ ± 3.32/₂
= 3+ 3.32 or 3 - 3.32
= 6.32 or - 0.32
how could you correctly rewrite the equation 4(5+3)=2(22-6) using the distributive property?
We can correctly rewrite the equation: 4(5+3) = 2(22-6) by distributing each side.
4(5+3) = 2(22-6)
4(8) = 2(16)
32 = 32
Once you finish distributing each side, you can check to see if it is equal on both sides.
In our case it is since they both equal 32 after distributing the terms.
Find the standard divisor to two decimal places (hundredth) for the given population and number of representative seats.
Population : 140,000
# seats : 9
A) 15,555.56
B) 17,055.56
C) 13,056
D) 14,055.56
E) 16,055
Answer:
A
Step-by-step explanation:
A divisor refers to a number by which another number is to be divided.
So what this question is practically asking us is that which of the values in the options to 2 decimal places is the result dividing the population by the number of seats
Thus we have;
140,000/9 = 15,555.55555 which to 2 decimal places is 15,555.56
A quality control inspector has determined that 0.25% of all parts manufactured by a particular machine are defective. If 50 parts are randomly selected, find the probability that there will be at most one defective part.
Answer:
9.941*10^-6
Step-by-step explanation:
Probability of at most 1 means not more than 1 defective= probability of 1 or probability of 0
Probability of 1 = 50C1(0.25)(0.75)^49
Probability= 50(0.25)*7.55*10^-7
Probability= 9.375*10^-6
Probability of 0
= 50C0(0.25)^0(0.75)^50
= 1(1)(0.566*10^-6)
= 0.566*10^-6
Total probability
= 9.375*10^-6+ 0.566*10^-6
= 9.941*10^-6
a man is 3 times as old as his son . the sum of their ages is 48 years .how old is the son ? how old is the dad?
Answer:
son is 12
dad is 36
Step-by-step explanation:
Say the son is x years old.
Then the father is 3x. Also 3x+x must be 48.
So 4x = 48 => x= 48/4 = 12
Let x be how old the son is. We know that the dad is 3 times older and their sum is 48. Creating an equation to represent this situation gives us:
[tex]x+3x=48[/tex]
[tex]4x=48[/tex]
Divide both sides by 4
[tex]x=12[/tex]
The son is 12 years old, but we want to find the age of the dad. Since we know the dad is 3 times older, multiply 12 with 3
[tex]12 \times 3 = 36[/tex]
The dad is 36 years old. Let me know if you need any clarifications, thanks!
Suppose that you have $100. You have two options for investing your money.
Option 1: Increase by $10 each year
Year
Amount
1
100
110
Type:
a =
b =
Answer:
Option One:
type : linear growth
a : 120
b : 130
Option 2:
type: linear growth
d : 121
e : 133
Step-by-step explanation:
its right on EDG 2020
Option One:
type: linear growth
a: 120
b: 130
Option 2:
type: linear growth
d: 121
e: 133
What is linear and exponential growth?Linear growth occurs with the aid of including an equal amount in each unit of time. An exponential increase happens while a preliminary population will increase by the same percent or issue over the same time increments or generations.
What is the distinction between linear and exponential?Linear and exponential relationships vary within the way the y-values change whilst the x-values increase with the aid of a steady quantity: In linear dating, the y-values have identical variations. In an exponential relationship, the y-values have identical ratios.
Learn more about Linear growth here: brainly.com/question/4025726
#SPJ2
Because of a manufacturing error, 3 cans of regular soda were accidentally filled with diet soda and placed into a 24-pack. Suppose that two cans are randomly selected from the 24-pack. Determine the probability that at least one contain regular soda.
Answer:
161/184 or 0.875
Step-by-step explanation:
Total number of cans = 24 cans
Total number of diet soda = 3 cans
Total number of regular soda = 21 cans
We are asked to find the probability that:that at least one contain regular soda if two cans are selected randomly
We have two ways for this happening
a) two of the cans are regular soda
b) one of the cans is regular , while one is diet
Hence,
Probability (that at least one contain regular soda) = Probability(that two of the cans are regular soda) + Probability ( one of the cans is regular , while one is diet)
Probability(that two of the cans are regular soda) = 21/24 × 20/23
= 35/46
Probability ( one of the cans is regular , while one is diet) = 21/24 × 3/23
= 21/184
Probability (that at least one contain regular soda) = 35/46 + 21/184
We find the Lowest common multiple of the denominators = 184
= 35/46 + 21/184
= (35 × 4) + (21 × 1)/184
= 140 + 21/184
= 161/184
= 0.875
Therefore, the probability that at least one can contains regular soda = 161/184 or 0.875
Consider the Equation y > 3x + 1 (a) Find an ordered pair that satifies the equation (b) Is the equation a Releation? explain (c) Is the equation a Function? explain
Answer:
(a) (1,5)
(b) Every subset of a cartesian product is a relation, therefore this is a relation.
(c) The relation IS NOT a function.
Step-by-step explanation:
(a)
(1,5)
Notice that 3(1) +1 = 4 < 5 therefore (1,5) is an order pair that satisfies the equation.
(b)
Every subset of a cartesian product is a relation, therefore this is a relation.
(b)
A relation is a function of the following condition holds
if (a,b) and (c,b) belong to the relation then (a=c)
In this case, (1,5), (0,5) belong to the relation but 0 is different than 5, therefore the relation IS NOT a function.
Type the correct answer in the box. Use numerals instead of words. What is the missing value in the inverse variation given in the table?
Answer:
48
Step-by-step explanation:
If x varies inversely as y, we have:
[tex]x \propto \frac{1}{y} \\\implies x = \frac{k}{y}[/tex]
When x=2, y=96
[tex]2 = \frac{k}{96}\\k=192[/tex]
When x=8, y=24
[tex]8 = \frac{k}{24}\\k=192[/tex]
Therefore, the constant of proportionality, k=192.
The equation connecting x and y is:
[tex]x = \frac{192}{y}[/tex]
When x=4
[tex]4 = \frac{192}{y}\\4y=192\\y=48[/tex]
The missing value in the inverse variation given in the table is 48.
Solve for x. Answer as an integer or simplified fraction. Please include steps. Thanks!
Answer:
x=40 degreesStep-by-step explanation:
According to the angle sum theorem, the interior angles of a triangle add up to 180 degrees:
So, we can use the following equation to find x:
x+(x+10)+(210-3x)=180
now add like terms:
x+x+(-3x)+10+210=180
-x+220=180
now isolate the variable:
-x=180-220
-x=-40
x=-40/-1
x=40/1
x=40
The answer is that: the measure of x is 40 degrees
what is 4 1/3 x 4 1/5=
Answer:
18 1/5
Step-by-step explanation:
Hey there!
Well to multiply them let's make them improper.
13/3 * 21/5
13*21 = 273
3*5 = 15
273/15
Simplified
18 1/5
Hope this helps :)
Answer:
[tex]\huge\boxed{4\dfrac{1}{3}\times4\dfrac{1}{5}=18\dfrac{1}{5}}[/tex]
Step-by-step explanation:
[tex]4\dfrac{1}{3}\times4\dfrac{1}{5}\\\\\bold{STEP\ 1}\\\text{convert the mixed numbers to the improper fractions}\\\\4\dfrac{1}{3}=\dfrac{4\times3+1}{3}=\dfrac{12+1}{3}=\dfrac{13}{3}\\\\4\dfrac{1}{5}=\dfrac{4\times5+1}{5}=\dfrac{20+1}{5}=\dfrac{21}{5}\\\\\bold{STEP\ 2}\\\text{simplify fractions}\\\\4\dfrac{1}{3}\times4\dfrac{1}{5}=\dfrac{13}{3}\times\dfrac{21}{5}=\dfrac{13}{1}\times\dfrac{7}{5}\\\\\bold{STEP\ 3}\\\text{multiply numerators and denominators}\\\\=\dfrac{13\times7}{1\times5}=\dfrac{91}{5}[/tex]
[tex]\bold{STEP 4}\\\text{convert the improper fraction to the mixed number}\\\\=\dfrac{91}{5}=\dfrac{90+1}{5}=\dfrac{90}{5}+\dfrac{1}{5}=18\dfrac{1}{5}[/tex]
The measure of ∠1 is 150°. What are the measures of ∠4, ∠3 and ∠2?
Answer:
∠1 is 150°
∠2 is 30°
∠3 is 150°
∠4 is 30°
Step-by-step explanation:
∠1 is vertically opposite to ∠3 so they are equal
360° - (150° + 150°) = 360° - 300° = 60°
∠2 and ∠4 must sum to 60°
Step-by-step explanation:
From the question
∠1 is opposite to ∠ 3 and vertically opposite angles are equal
So
∠1 = ∠ 3
That's
∠ 3 = 150°∠ 3 and ∠ 4 are on a straight line and angles on a straight line add up to 180°
So to find ∠4, subtract ∠3 from 180°
That's
∠ 4 = 180 - ∠ 3
∠ 4 = 180 - 150
∠ 4 = 30°Since ∠ 4 and ∠ 2 are opposite they are also equal
That's
∠ 4 = ∠ 2
Therefore
∠ 2 = 30°Hope this helps you
which of the following is a mathematical representation of a function that provides detailed information but can become unwieldy?
Answer:
C. Equation
Step-by-step explanation:
An equation generally provides the most specific information about a function. However, it cannot always be used for certain purposes—such as finding a specific inverse function value.
In the case of equations that are infinite series, even evaluating the function can become difficult when the series converges slowly.
The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model. The silver model requires 1 minute in a grinder and 3 minutes in a bonder. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder. Because of maintenance procedures, the grinder can be operated no more than 30 hours per week and the bonder no more than 50 hours per week. The company makes $5 on each silver pen and $7 on each gold pen. How many of each type of pen should be produced and sold each week to maximize profits?
Answer:
Optimal production = 600 gold pens
Revenue = 600*7 = $4200 gold pens
Step-by-step explanation:
The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model.
A. The silver model requires 1 minute in a grinder and 3 minutes in a bonder.
B. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder.
Because of maintenance procedures,
C. the grinder can be operated no more than 30 hours per week and
D. the bonder no more than 50 hours per week.
The company makes
E. $5 on each silver pen and
F. $7 on each gold pen.
How many of each type of pen should be produced and sold each week to maximize profits?
Solution:
We will solve the problem graphically, with number of silver pens, x, on the x axis, and number of gold pens, y, on the y axis, i.e.
1. From A and C, the maximum number of silver pens
x <= 30*60 / 1 = 1800 and
x <= 50*60 /3 = 1000 ....................(1) bonder governs
2. from A & D, the maximum number of gold pens
y <= 30*60 / 3 = 600 .....................(2) grinder governs
y <= 50*60 / 4 = 750
3. From D,
x + 3y <= 30*60 = 1800 ...................(limit of grinder) ..... (3)
3x + 4y <= 50*60 = 3000 .................(limit of bonder) .......(4)
Need to maximize profit,
Z(x,y) = 5x+7y, represented by parallel lines y = -5x/7 + k such that all constraints of (3) and (4) are satisfied.
The maximum is obtained when Z passes through (360,480), i.e. at intersection of constraints (3) and (4). Using slope intercept form,
(y-480) = -(5/7)(x-360)
or y=-(5/7)x + (737+1/7) [the purple line] which violates the red line, so not a solution.
Next try the point (0,600)
(y-600) = -(5/7)(x-0), or
y = 600 - (5/7)x [the black line]
As we can see all point on the black (in the first quadrant) satisfy the constraints, so it is a feasible solution, and is the optimal solution, with a revenue of
Revenue = 600*7 = 4200 gold pens