Answer:
Step-by-step explanation:
To put a ratio in its lowest terms, we need to divide both terms of the ratio by their greatest common divisor (GCD). The GCD of 1500 and 1200 is 300, which is the largest number that divides both numbers evenly.
Dividing both terms of the ratio by 300, we get:
1500 / 300 : 1200 / 300 = 5 : 4
So, the ratio 1500:1200 in its lowest terms is 5:4.
50 pair of tennis shoes at $85 a pair with terms 4/10, 2/30, n/60. the invoice was dated for october 15. payment was sent in october 28, what was the total amount of the check
Answer:
Step-by-step explanation:
The terms "4/10, 2/30, n/60" indicate that the buyer can take a discount of 4% if they pay within 10 days from the invoice date, or pay the full amount within 30 days from the invoice date. If the payment is made after 30 days, the buyer must pay the full amount plus any late fees that may apply.
Since the invoice was dated October 15 and the payment was sent on October 28, the payment was made within 30 days from the invoice date, so the buyer cannot take the 4% discount.
The total cost of 50 pairs of shoes at $85 per pair is 50 * 85 = $4250.
Therefore, the total amount of the check would be $4250, which is the full amount of the purchase price without the 4% discount.
Will is moving from Boston to Philadelphia which is 300 miles away. He is traveling at an
In ADEF, J is the intersection of the three medians. If EI = 33, find JI.
D
Q
H
F
The value of JI in the given triangle is 11.
What is a triangle?A triangle is a polygon with three sides, vertices and angles.
Given that, in a triangle DEF, J is the intersection of the three medians.
EI = 33, we are asked to find the value of JI,
Since, all the median is intersecting at J, therefore, J is the centroid.
We know that, the centroid divides each median into two parts, which are always in the ratio 2:1.
Therefore,
Let, EI = 3x,
JI = x,
Therefore, JI = 11
Hence, the value of JI in the given triangle is 11.
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The complete question is :
In Δ DEF, J is the intersection of the three medians. If EI = 33, find JI.
Figure is attached
Solve d+5/-2<=-3/2 please help I will give brainly
Answer:
Step-by-step explanation:
inequality form
d≤ 1
Interval Notation:
(−∞,1]
NEED HELP ASAP!!!
Due today
Answer:
20 cubic yards
Step-by-step explanation:
You want to know the volume in cubic yards of a layer of topsoil that is 6 inches deep over an area 31 feet by 34 feet.
UnitsYou know that ...
36 inches = 1 yard3 feet = 1 yardThen the dimensions of the volume being applied are ...
6 inches = 6/36 yards
31 feet = 31/3 yards
34 feet = 34/3 yards
VolumeThe volume is the product of the dimensions of the space:
V = LWH
V = (31/3 yd)(34/3 yd)(6/36 yd) ≈ 19.519 yd³
About 20 cubic yards are needed to fill the garden.
Sara can type 90 words in
4 minutes. About how many words
would you expect her to type in
10 minutes at this rate?
[tex]\begin{array}{ccll} words&minutes\\ \cline{1-2} 90 & 4\\ x& 10 \end{array} \implies \cfrac{90}{x}~~=~~\cfrac{4}{10} \\\\\\ \cfrac{ 90 }{ x } ~~=~~ \cfrac{ 2 }{ 5 }\implies 450=2x\implies \cfrac{450}{2}=x\implies 225=x[/tex]
In Iceland, the temperature drops when the sun goes down. The temperature at 5:00 is 5°C. By 9:00, the temperature had dropped 24°. If the temperature dropped at a constant rate, how much did it drop per hour?
If the temperature dropped at a constant rate, it would have dropped 4°C per hour. This can be calculated by taking the difference in temperature (24°C) and dividing it by the number of hours that passed (4 hours).
Which of the following equations represents a linear function? Please show the steps of the answer! Thank you
Answer:
2nd choice y = 1/2x - 5
Step-by-step explanation:
y = 1/2x - 5 is the only function listed that if you graph it, it makes a straight line. A linear function forms a straight line when it is plotted on a graph.
The first and last choices are number values of x.
The 3rd choice, if you graph it, makes a parabola.
Answer:
Second option:
[tex]y = \dfrac{1}{2}x -5[/tex]
Step-by-step explanation:
A linear function should have y as a function of x (or x as a function of y) and the degree of the function (the highest power has to be 1)
Both x and y must be present to make it a linear function
General slope intercept form is y = mx + b where m = slope, b = y-intercept
With these restrictions the second option is the correct one
[tex]y = \dfrac{1}{2}x -5[/tex]
This line is in slope intercept form y = mx + b where m = slope(in this case 1/2) and y-intercept b(in this cae -5)
Option 1: x = 3 is a straight vertical line parallel to the y-axis. Such a line has a slope of ∞
Option 3 is a function with degree 2 and is a quadratic function
Option 4 : 3x - 6 = 4==> 3x = 6 + 4 = 10 or x = 10/3, again another vertical line with slope = ∞
A true-false quiz contains six questions. In how many ways can a student answer the questions if the student answers two of the questions with "false" and the other four with "true"?
Answer: In each question you have two options, T and F. Then in 6 questions you have 2 options for the first, two for the second, two for the third... At the end you get 2·2·2·2·2·2 = 26 options and 26 = 64.
Step-by-step explanation:
(9+w) (2w+3)=0
If there is more than one solution, please seperate with commas
if TAN a =21/29 calculate the values of seca - coseca/seca+coseca
The values of sec a - cosec a/sec a+cosec a is 4/25.
Trigonometric ratios:The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
In a right-angled triangle,
Sin θ = Opposite Side /HypotenuseCos θ = Adjacent Side /HypotenuseTan θ = Opposite Side/Adjacent Side Sec θ = 1/cos θCosec θ = 1/sin θHere we have
tan A = 21/29
As we know Tan θ = Opposite side/Adjacent side
=> Opposite side = 21
=> Adjacent side = 29
In a right-angle triangle,
=> Hypotenuse² = Opposite side² + Adjacent side²
=> Hypotenuse² = 21² +29²
=> Hypotenuse² = 441 + 841
=> Hypotenuse² = (35.8)²
Cos a = Adjacent side /Hyopenuse = 29/ 35.8
Sin a = Opposite side/Hypotenuse = 21/35.8
The given expression can be solved as follows
=> [tex]\frac{seca - coseca}{seca+coseca } = \frac{ \frac{1}{cos a}-\frac{1}{sina} }{\frac{1}{cos a }+\frac{1}{sin a} }[/tex]
=> [tex]\frac{ \frac{sin a - cosa}{cos a sn a} }{\frac{sin a + cos a}{cos a sin a} }[/tex]
=> [tex]\frac{sin a - cosa}{cos a+ sin a}[/tex]
=> [tex]\frac{ \frac{21}{35.8} - \frac{29}{35.6} }{\frac{29}{35.8} + \frac{21}{35.8} }[/tex]
=> [tex]\frac{21- 29}{29+21}[/tex]
=> [tex]\frac{8}{50}[/tex]
=> [tex]\frac{4}{25}[/tex]
Therefore,
The values of sec a - cosec a/sec a+cosec a is 4/25.
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The original price of a pair of running shoes was $95.00. They were on sale at 25% off, but the marked price was $73.25. Is this the correct price? Explain.
No, the marked price of $73.25 is not correct.
To calculate the sale price, we start by multiplying the original price by the discount percentage:
$95.00 * 0.25 = $23.75
This means that the original price of $95.00 should be reduced by $23.75 to find the sale price:
$95.00 - $23.75 = $71.25
Since the marked price is $73.25, this means that the store made a mistake and overpriced the shoes by $2.00. The correct sale price should have been $71.25.
Is one bank ALWAYS better? What factors might affect which bank has the better fee
structure?
No one bank is not always better. Factors such as the fees and the charges in one bank may differentiate it from another bank.
What may cause a bank to be better than another bank?No, one bank is not always better than another. The best bank for an individual depends on a variety of factors, including their financial needs and preferences, location, and the fees and charges associated with different banks.
For example, one bank may have lower fees for checking accounts but higher fees for ATM withdrawals or international transactions, while another bank may have higher fees for checking accounts but lower fees for other services.
Other factors that might affect which bank has the better fee structure include the type of account, the minimum balance required to avoid fees, and the level of customer service provided by the bank. Ultimately, the best bank is the one that meets an individual's financial needs at the lowest cost.
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Multiply the following radicals and simplify your answer.
2√6⋅−3√12
Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $
3.00 for rolling a 1 or a 3, nothing otherwise. What is your expected net winnings?
for
lingun?
Answer:
21.7% to win $3, thats ~1/5
Step-by-step explanation:
100/6 = 10.(6) % to roll for each number (let it be just ~10.7)
for rolling a 3 or a 1 u will get $3
10.7 + 10.7 = 21.7% to win $3, thats 1/5
A designer creates a drawing of a triangular sign on centimeter grid paper for a new business. The drawing has sides measuring 3 cm, 4 cm, and 5 cm, and angles measuring 37°, 53°, and 90°. To create the actual sign shown, the drawing must be dilated using a scale factor of 80.
Answer:
240 cm, 320 cm, 400 cm
Step-by-step explanation:
The drawing length multiplied by the scale factor gives the real length.
3 cm × 80 = 240 cm
4 cm × 80 = 320 cm
5 cm × 80 = 400 cm
Answer: 240 cm, 320 cm, 400 cm
5.3A Find Two Numbers Whose Product and Sum is as Indicated
For product=6 and sum=7, the numbers or integers are 1 and 6.
What exactly are integers?
In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.
now,
As given product=6 and sum=7
make factors for 6 i.e 1,2,3,6
from these choose the numbers whose sum=7
and they are 1,6.
Hence,
For product=6 and sum=7, the numbers are 1 and 6.
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What is the doubling time for the investment? Round answer to 1 decimal place.
The amount of money in an investment is modeled by the function A(T)=650(1.0455)^T. The variable A represents the investment balance in dollars, and T the number of years.
The doubling time for the investment as required to be determined is; 15.58 years.
What is the value of the investments doubling time?It follows from the task content that the model function is;
A(T)=650 (1.0455) ^T
For doubling time;
2 = (1.0455)^T
ln (2) = T ln (1.0455)
T = ln 2 / ln (1.0455)
T = 15.58 years.
Ultimately, the doubling time of the investment as required is; 15.58 years.
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Write the set using set-builder notation
(9, 18, 27, 36, ...}
How do i do this
The set builder notation is A = { 9x | x ∈ N } which is a set of all x’s containing multiples of 9
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the set be represented as A
Now , the value of A is
A = { 9 , 18 , 27 , 36 , ... }
The set A contains all the positive multiples of 9
So , let x be the set of natural numbers and the value of A is
A = { 9x | x ∈ N } , and
A = set of all x’s containing multiples of 9
Hence , the set builder notation is { 9x | x ∈ N }
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1. Is Event 1 and Event 2 Mutually Exclusive of each other? Event 1: Pre- Schooler is a girl Event 2: Pre- Schooler prefers the color blue to the color pink Select one: a. No, A girl pre-schooler can prefer the color blue to the color pink. b. Yes, The gender of pre-schooler has no affect on color preference c. Yes, Girls prefer the color pink to the color blue 2. 70 preschoolers were asked whether they preferred blue or pink. 35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color. Assuming one of the pre-schoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.
The probability of choosing a preschooler who is a girl and prefers the color blue is 0.3 or 30%.
The total number of preschoolers who were asked about their color preference is 70. Out of these, 35 girls chose pink, 15 girls chose blue, 5 boys chose pink, and 15 boys chose blue.
To find the probability of choosing a girl who prefers blue, we need to use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Here, the favorable outcome is choosing a girl who prefers blue. We can see that 15 girls chose blue as their preferred color. Out of these, we need to choose a girl, so the total number of favorable outcomes is 15.
The total number of outcomes is the total number of preschoolers, which is 70. Out of these, the number of girls is 35+15=50. Therefore, the total number of outcomes where a girl can be chosen is 50.
Putting these values in the formula, we get:
Probability = 15/50 = 0.3
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Complete Question;
70 preschoolers were asked whether they preferred blue or pink.
35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color.
Assuming one of the preschoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.
Complete the sentence below.
0.075 is a hundred times smaller than
Answer:
0.0075
Step-by-step explanation:
The lengths of nails produced in a factory are normally distributed with a mean of 6.13
centimeters and a standard deviation of 0.06
centimeters. Find the two lengths that separate the top 7%
and the bottom 7%
. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
The two lengths that Bottom 7%: L= 6.04 cm
Top 7%: L= 6.22 cm
What does "z-score" mean?
The Z-score provides information on how far a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score.
The level of variability within a particular data collection is effectively reflected in the standard deviation.
Mean length of the population (μ) = 6.13 cm
Standard deviation (σ) = 0.06 cm
The z-score for any given length 'X' is
Z = X - μ/σ
What we want to know is the length at the 7-th percentile and at the 93-rd percentile.
According to a z-score table, the 7-th percentile has a correspondent z-score of -1.476 and the 93-rd percentile has a z-score of 1.476. Therefore, the bottom 7% and top 7% are separated by the following lengths
Z(Xb) = Xb - μ/σ
- 1.476 = Xb - 6.13/0.06
Xb = 6.04
z(Xt ) = Xt - μ/σ
1.476 = Xt - 6.13/0.06
Xt = 6.22
Bottom 7%: L= 6.04 cm.
Top 7%: L= 6.22 cm.
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Elmo wrote Kris a check for $601.73, and Kris deposited the check into her checking account. Where was Kris' signature?
A. On neither the front of the check nor the back of the check
B. On both the front of the check and the back of the check
C. Only on the back of the check
D. Only on the front of the check
The location of Kris' signature on the $601.73 check Elmo wrote to Kris and which Kris deposited into her checking account is on the back of the check. The correct option is option C.
C. Only on the back of the check
What is a checking account?A checking account is an account opened at a financial institution into which deposits and withdrawals can be made by a customer. A checking account can also be referred to as a transaction account, a credit unions share draft account, demand deposit account or current account.
The amount of check Elmo wrote Kris = $601.73
The amount Kris deposited into her checking account = The check Elmo issued to her
The location to sign before depositing a check into a checking account is at the back of the check, including informing the cashier that the specified check is to be deposited into the checking account.
The correct option is therefore option C.
C. Only on the back of the check
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what is the value of Z in this figure Enter your answer in the box
Using the a pair of adjacent angles, we will see that:
Z° = 137°
What is the value of z on the diagram?When we have an intersection between two lines, we know that any pair of adjacent angles (they share a side) are congruent angles, thus, their measures add up to 180°.
Then here we can write a linear equation for z.
z + 43 = 180
Solving that for z, we will get:
z = 180 - 43
z = 137
That is the measure of the angle.
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Two hundred college students were recently asked if they participated in music or sports. 127 students said they were
involved in music. 78 students said they participated in both activities, while 20 students did not participate in either.
How many students participated in only music?
How many students participated in only sports?
How many students were involved in music or sports?
Using Venn diagram, 49 students participated in only music, 29 students participated in only sports, and 156 students were involved in either music or sports.
What is the number of students that participated in only musicLet's use a Venn diagram to represent the information given:
We know that there are 200 students in total, and we can use the information given to fill in the numbers in the Venn diagram.
a.
127 students were involved in music, including 78 who were also involved in sports, so 127 - 78 = 49 students participated in only music.
b.
78 students participated in both music and sports, so 78 - 49 = 29 students participated in only sports.
20 students did not participate in either activity.
c.
The total number of students involved in music or sports is the sum of the number of students in each circle: 49 + 29 + 78 = 156.
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Help!!
Write an equation to show the total cost, y, for x months.
YOU WIL GET BRAINLIEST!!
The equation to represent the total cost, y, for x months is y = 12x + 30.
From the given table, we can observe that the total cost increases by $12 for each additional month of usage.
This means that the rate of change, or the slope of the equation, is $12 per month.
We can represent this relationship using the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (rate of change) is $12, and the y-intercept can be determined by examining the table. When x = 0 months, the total cost is $30. Therefore, the y-intercept is $30.
Putting it all together, the equation to represent the total cost, y, for x months is:
y = 12x + 30
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NEED PLS THANK YOU DUE TODAY
Now , to find the area
Total area of figure = Area of first Triangle + Area of second triangle
The area of the triangle = ( 1/2 ) x Length x Base
Total area of figure = ( 1/2 ) x ( 36 x 15 ) + ( 1/2 ) x ( 15 x 8 )
= ( 1/2 ) x 540 + ( 1/2 ) x 120
= 270 + 60
= 330 inches²
Therefore , the value is 330 inches²
Hence , The area of the figure is 330 inches²
∠A=6x−35 ∘ start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 35, degrees, end color #11accd ∠ � = 3 � + 5 3 ∘ ∠B=3x+53 ∘
73 degrees is the equivalent meausure of m<A
Solving line geometryFrom the given line geometry below, the sum of the adjacent angles is 180 degrees as shown:
m∠A + m∠B = 180
Given the following
∠A = 6x - 35
∠B = 3x + 53
Substitute the given parameters
6x - 35 + 3x + 53 = 180
9x + 18 = 180
9x = 180 - 18
9x = 162
x = 162/9
x = 18
Determine the measure of <A
<A = 6x - 35
<A = 6(18) - 35
<A = 108 - 35
<A = 73 degrees
Hence the measure of angle A from the given diagram is 73 degrees
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Write System of Equations from Context
Kennedy has $0.81 worth of pennies and nickels. She has 9 more nickels than
pennies. Write a system of equations that could be used to determine the number of
pennies and the number of nickels that Kennedy has. Define the variables that you
use to write the system.
Let __=_________
Let__=___________
System of Equations:
_________________
_________________
I will give brainliest and ratings if you get this correct
The quotient rule is proved below.
What is derivative of a function?In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
Given is the expression -
Q(x) = F(x)/G(x)
Quotient rule -Quotient rule in calculus is a method used to find the derivative of any function given in the form of a quotient obtained from the result of the division of two differentiable functions. Mathematically, for a function f(x), we can write -
f'(x) = [u(x)/v(x)]' = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²
Proof -Now, let f(x) = u(x) and g(x) = v(x).
Q(x) = u(x)/v(x)
Q(x) = u(x) v⁻¹(x)
Using the product rule -
Q'(x) = u'(x) v⁻¹(x) + u(x) {d/dx v⁻¹(x)}
Q'(x) = u'(x) v⁻¹(x) + u(x) (-1)(v(x)⁻²) v'(x)
Q'(x) = u'(x)/v(x) - u(x)v'(x)/v²(x)
Q'(x) = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²
Therefore, the quotient rule is proved above.
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