There are 6 pennies in a total of 150 coins.
Given that,
Ninety of the 150 coins are quarters. 40 percent of the remaining coins are nickels, with the remainder being dimes and pennies.
and also,
For every penny, there are five dime.
Total = 150 coins
Out of it, 90 are quarters so the remaining coins are 60
It is said that,
In that 60 coins 40% are nickels which means
40% of 60 is 24
So remaining coins are 36 (by subtracting 24 from 60)
It is said that there are 5 dimes for every penny which means
Using Algebra,
x + 5x = 36
6x= 36
x= 6
Therefore, there are 6 pennies in a total of 150 coins.
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A line has a slope of -2/3 and passes through the point (-3,8). What is the equation of the line?
A. y = -2/3 x + 6
B. y = -2/3 x + 8
C. y = 6x - 2/3
D. y = 8x - 2/3
Answer:
A
Step-by-step explanation:
denise did 7/8 of the problems on her quiz correctly and five incorrectly. how many problems were on the test
The quiz consists of 40 problems and it solved by a linear equation.
What is the linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
Assume that the quiz consists of n problems.
Denise did 7/8 of the problems correctly.
If the total number of problems of the quiz is n, the number of answers that are correct is (7/8)× n.
The number of incorrect problems are 5.
Total number of problems those are done by Denise is { (7/8)× n}+5.
Assume that Denise attempts all problems.
Now making a linear equation:
{ (7/8)× n}+5 = n
(7n)/8+5 = n
(7n+40)/8 = n
(7n+40) = 8n
Subtract 7n from both sides:
7n+40 -7n = 8n - 7n
40 = n
The number of problems in the quiz is 40.
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.
How do you find the maximum and minimum value of the function?
Calculus can be used to find the critical point, or the x-value of the vertex, by taking the derivative of the function, or f'(x). To determine the critical point, we shall set the function's first derivative to zero and solve for x. This point's maximum or minimum value can be determined by taking the second derivative, or f"(x). The second derivative will have a minimal value if it is positive. The second derivative will be the highest value if it is negative.
Given function:
[tex]-3x^2+18x+3[/tex]
To find the maximum and minimum value of the function use second derivative test.
On differentiating the above function we get,
-6x + 18
Now, find critical point
-6x + 18 = 0
-6x = - 18
x = - 18/-6 = 3
x = 3
Here, x = 3 is the critical point. Now again differentiate the above function we get,
-6
As , [tex]f^{''}(x)[/tex] < 0 , therefore x = 3 will given a maximum value of function and maximum value is
f(3) = [tex]-3(3)^2+18x+3 = -3(9) + 18(3) + 3 = -27 + 54 + 3 = 27 + 3 = 30[/tex]
Hence , function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.
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Make d the subject of the formula h=d/3+2
Answer:
d = 3h - 6
Step-by-step explanation:
h = [tex]\frac{d}{3}[/tex] + 2 ( multiply through by 3 to clear the fraction )
3h = d + 6 ( subtract 6 from both sides )
3h - 6 = d
what's the distance between points A and B
Answer:
AB = 10 units============
GivenEndpoints A(-8, -4) and B(2, - 4)Find the length of ABSince both points have same y-coordinate, the distance between the points is the difference of x-coordinates:
AB = 2 - (-8) = 2 + 8 = 10 unitsFind the missing base.
Write your answer as a whole number.
2=100
The missing base for the expression x² = 100 is given by:
± x = 10.
How to find the missing base?The expression in this problem is given as follows:
x² = 100.
The missing base is represented by the variable x, hence we have to solve the above expression x² = 100 for the variable x.
To solve for x, we need to isolate the variable x, applying the inverse operation to the second power, which is the square root, hence the variable x is isolated as follows:
x = plus/minus square root of 100.
The plus/minus sign is necessary because the x-squared function is even, then the missing base is obtained as follows:
x = ± 10.
Plus/minus 10 because both of these statements are true:
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Toby submitted the following work when asked to convert 12 2/3 to an improper fraction
Answer:
a) He didn't add 2.
b) 38/3
What’s the answer plss
Answer:
<ABD = 67.17
Step-by-step explanation:
Comment
This requires 2 steps.
Find <AFind <ABDFinding <A
<A is found by taking the inverse tangent of the ratio 8/19.
<A = tan-1*(8/19)
<A = 22.83 degrees. We'll round it later.
Finding <ABD
You have to use 2 facts here.
All triangle angles add up to 180 degrees.
You find the third angle by subtracting the other 2.
<A = 22.83 Found above
<ADB = 90 degrees Given
<ABD = ?
Equation
< A + <ADB + <ABD = 180
Solution
22,83 + 90 + <ABD = 180 Combine the left
112.83 + <ABD = 180 Subtract 112.83 from both sides.
112.83-112.83 +<ABD = 180 - 112.83 Combine
<ABD = 67.17
The answer to the nearest degree is 67.
help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!
Answer:
The rocket reaches its maximum height at 2.25 seconds.
It’s maximum height is 88 feet.
This can be found by finding the derivative of the function and setting it to zero.
-16x² +72x + 7
Taking first derivative and setting to zero:
-32x + 72 = 0
x = -72/-32=2.25
Find the height when x is 2 seconds by substituting this value into the original function:
-16 * (2.25)² + 72 * 2.25 + 7 = 88
Therefore the maximum turning point of the parabola will be (2.25, 88)
find the unit rate of $36 : 1/2 hour
Answer:
$72 / hr
Step-by-step explanation:
$36 / (1/2 hr ) = $72 per hour
Tran planned a rectangular pool and made a scale drawing using centimeters as the unit of measurement. He originally planned for the length of the pool to be 40 m but decided to change it to 32 m. If the length of the pool in his scale drawing is 8 cm, which statement about the change of scale is true?
One cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.
One cm represented 40 m in the first scale, but now 1 cm represents 32 m in the second scale.
One cm represented 1 m in the first scale, but now 1 cm represents 5 ft in the second scale.
One cm represented 4 m in the first scale, but no
The true statement about the change of scale is 1 cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Given that, Tran planned a rectangular pool and made a scale drawing using cm as the unit of measurement. He originally planned for the length of the pool to be 40 m but decided to change it to 32 m. If the length of the pool in his scale drawing is 8 cm,
The scale factor of drawing to original pool was 1/5 before changing the length but when length changed to 32 m scale factor now is 1/4
Hence, The true statement about the change of scale is 1 cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.
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write and equation for a line that's parallel to y=2x-3 that passes through (-1,6)
Answer:
y=2x+8
Step-by-step explanation:
The slope must be the same so the equation so far is y=2x+b
To find b, you have to multiply the given x value (-1 is the given x value) and then see how much you have to add to reach the given y value (aka 6)
-1*2=-2
6--2=8
b=8
That means that the equation is y=2x+8
How will you solve problems involving equations of circles and coordinates?
NEED ASAP
An equation is a mathematical statement showing the equality of two
opposite variables
How to determine the equation of the circle using coordinates?
The equation of a circle is determined by the function r²=(x-x1)² +(y-y1)²
where :
(x1,y1,) marks the centre of the circlex,y marks the points on the circumference of the circumference of the circler marks the radius of the circlethen, the last thing is to write the equation of the circle and input the values of the coordinates to arrive at your answer,
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I'm having trouble with this, which one is it?
The information illustrated regarding the numbers shows that it's a C. Direct variation.
What is a direct variation?A direct variation means the variation that has a constant of proportionality.
In this case, when x is 256, y is 32. The constant is 32/256 = 1/8
When y = 6, x = 48. The constant is also 6/48 = 1/8.
Therefore, it's a direct variation.
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what is the probability that a positive integer not exceeding 100 selected at random is divisible by 5 or 7
Answer:
So, the probability of selecting a number from 1 to 100 that is divisible by 5 or 7 is 0.32.
Hope this helped!
Solve the following:
a) a/5+3=8
b) 3b/7-1=5
a) a/5 + 3 = 8
Step 1 : Minus both sides by 3
a/5 + 3 - 3 = 8 - 3 -> a/5 = 5
Step 2 : Multiply both sides by 5
a/5 x 5 = 5 x 5 -> a = 25.
b) (3b)/7 - 1 = 5
Step 1 : Add both sides by 1
(3b)/y - 1 +1 = 5 + 1 -> (3b)/7 = 6
Step 2 : Multiply both sides by 7
(3b)/7 x 7 = 6 x 7 -> 3b = 42
Step 3 : Divide both sides by 3
3b : 3 = 42 : 3 -> b = 14.
a hospital director is told that 54% of the treated patients are insured. the director wants to test the claim that the percentage of insured patients is below the expected percentage. a sample of 200 patients found that 100 were insured. find the value of the test statistic. round your answer to two decimal places.
The value of test statistic is -1.14
Define Standard error.
The standard error (SE)of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).
Null Hypothesis
P = 0.54
Alternate Hypothesis
P < 0.54
For 0.05 level , the value of Z = 1.645
Decision rule ,
reject null Hypothesis if test statistic Z < -1.645
sample size (n) = 200
sample success (x) = 100
Standard error SE = √(p * (1 - p) / n
= √0.54 * (1 - 0.54) / 200
Standard error SE= 0.0352
Sample proportion (р) = x/n
= 100 / 200 ⇒ 0.5
test statistic Z = (р - P) / SE
= (0.5 - 0.54) / 0.0352
test statistic Z = -1.136 or -1.14
Therefore, the value of test statistic is -1.14
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help meeeeeeeeeeeeeee pleaseee
The table of solutions should be completed based on the given equation (y = 2x²) as follows:
x y_
-2 8
-1 2
0 0
1 2
2 8
Also, a graph of the solution to the given equation is shown in the image attached below.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.
Next, we would complete the table based on the given equation as follows:
When x = -2, the value of point y is given by:
y = 2x²
y = 2(-2)²
y = 2 × 4
y = 8
When x = -1, the value of point y is given by:
y = 2x²
y = 2(-1)²
y = 2 × 1
y = 2
When x = 0, the value of point y is given by:
y = 2x²
y = 2(0)²
y = 2 × 0
y = 0
When x = 1, the value of point y is given by:
y = 2x²
y = 2(1)²
y = 2 × 1
y = 2
When x = 2, the value of point y is given by:
y = 2x²
y = 2(2)²
y = 2 × 4
y = 8
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Simplify by expressing fractional exponents instead of radicals 8 sqrd x^2 y^4
After the use of fractional exponents give us the value 8√(x²y⁴) is 2³(x²y⁴)¹/₂.
Exponent:
Exponent is refers the way of writing the words, "raised to the power". And it is used to show that a number has been raised to a certain power.
Given,
Here we have the expression 8√(x²y⁴).
Now, we need to simplify the fractional exponents.
When we rewritten the expression like the following,
=> 8√(x²y⁴)
While we looking at these expression we know that, the number 8 can be written as the multiple of 2,
So, it can be written as,
=> 8√(x²y⁴) = 2³√(x²y⁴).
So, in the simplified form it can be written as,
=>8√(x²y⁴) = 2³(x²y⁴)¹/₂.
Therefore, the simplified form is 2³(x²y⁴)¹/₂.
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mr. bray prepares a list of 434343 us presidents, 888 of whom died in office. then 181818 of his students each select a president at random (there can be repeats) for their creative writing assignments. what is the probability that at least one of the students select a president who died in office? round your answer to the nearest hundredth.
There is a 0.97541 or 97.541% probability that at least one student will choose a president who passed away in office.
Take into account the details offered.
43 US presidents are listed by Mr. Bray, 8 of them passed away while in office.
Consequently, p= 8/43.
If 8 of the 43 presidents died while in office, then 43-8=35 presidents survived.
q= 35/43
Let X represent how many presidents have passed away while in office.
The probaility that at least one student will choose a president who passed away in office is:
P(X[tex]\geq[/tex]1 ) = 1 -P(X=0)
P(X[tex]\geq[/tex]1 ) = 1 -¹⁸c₀(8/43)⁰(35/43)¹⁸
By using Combinations Formula,
By solving we get,
P(X[tex]\geq[/tex]1 ) = 0.97541
As a result, there is a 0.97541 or 97.541% chance that at least one student will choose a president who passed away in office.
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Write the fraction or mixed number as a percent . 6/25
Answer:
24%
Step-by-step explanation:
6/25 is also the same as 24/100 because
(6/25)*(4/4)=24/100
Since the denominator is 100, the numerator is the percentage.
6/25=24%
Answer:
24%
Step-by-step explanation:
One way to figure this out is to multiply the denominator by 4 so that it becomes 100. This makes it easy to see what the percentage will be.
6/25 x 4/4 = 24/100
6/25 = 24%
30°
(5y-8)°
(6x-2)°
(11x-9)
72⁰
Answer:
x = 7°y = 18°Step-by-step explanation:
Find x:-
[tex]\sf 11x-9+72+6x-2=180[/tex]
[tex]\sf 17x+61=180[/tex]
[tex]\sf 17x=119[/tex]
[tex]\sf x=7[/tex]
Find y:-
[tex]\sf 30+11(7)-9+5y-8=180[/tex]
[tex]\sf 5y+90=180[/tex]
[tex]\sf 5y=90[/tex]
[tex]\sf y=18[/tex]
So, therefore, x = 7° & y = 18°!!
____________________
Hope this helps!
Have a great day! :)
A collector of rare books has a first-edition book worth $262, which he anticipates will grow in
value at a rate of 15% per year. How much will this book be worth 10 years from now?
If necessary, round your answer to the nearest cent.
Que
ans
2
The worth of the book after 10 years is $1061.1
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First edition book worth = $262
Rate of increase per year = 15%
The worth of the book after t years can be given by the expression.
= 262 x [tex]1.15^{t}[/tex]
Now,
The worth of the book when t = 10.
= 262 x [tex]1.15^{10}[/tex]
= 262 x 4.05
= $1061.1
Thus,
The book is worth $1061.1 after 10 years.
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Need help
Solve 4(x-5) = 18
Answer:
x = 19/2 or 9.5
Step-by-step explanation:
a) Distribute.
(4)(x) + (4)(−5) = 18
4x + −20 = 18
4x − 20 = 18
b) Add 20 to both sides.
4x − 20 + 20 = 18 + 20
4x = 38
c) Divide both sides by 4.
4x/4 = 38/4
x = 19/2 or 9.5
Answer:
9.5 or 19/2
Step-by-step explanation:
4 ( x - 5 ) = 18
Step 1 : Divide 4 on both sides.
x - 5 = 18/4
x - 5 = 4.5
Step 2 : Add 5 on both sides.
x = 4.5 + 5
x = 9.5
Value of x in fraction = 95/10 = 19/2
Value of x in decimal = 9.5
Please help!! Im so confused on this and need help badly
Answer: 11 months
Step-by-step explanation:
You do this by 73 times 11 equals 803
Then 49 times 11 equals 539 then add on the registration fee and it equals to 779 which is less than 803
two cars start moving from the same point. one travels south at 60 mi/h and the other travels west at 25 mi/h. at what rate is the distance between the cars increasing three hours later? 3 hours
The distance between the two cars varies at a speed of 65 m/h after two hours.
Let y represent the car's southward travel distance.
Let x be the distance traveled by the westbound automobile.
Allow a to be the distance between the two vehicles.
A right-angled triangle can be used to symbolize these three distances. So, we can state:
a^2 = x^2 + y ^2
Given that the distances vary with respect to time, let's make a distinction.:__________(1)
2a da/dt = 2x dx/dt +2y dy/dt
Rate of distance change between two cars, da/dt
The car is traveling west (dx/dt) at 25 m/h, while the car traveling south (dy/dt) is traveling at 60 m/h.
Therefore:
dy/dt = 60 m/h and dx/dt = 25 m/h
The separation between the two cars will be after two hours:
y = 3* 60 = 180 miles
x = 3 * 25 = 75 miles
Therefore:
a^2 = x^2 + y ^2
a^2 = 75 ^2+ 180 ^2
a= [tex]\sqrt{5625 + 32400}[/tex]
a= 195
From (1):
195(da/dt) = 75(25) + 180(60)
195(da/dt) = 1875 + 10800 = 12675
da/dt = 12675 / 195 = 65 m/h
As a result, after two hours, the two automobiles' separation is varying at a speed of 65 m/h.
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Determine the length of the line segment shown. line segment from negative 5 comma 5 to 3 comma negative 1 6 units 8 units 10 units 36 units
fist gets brainlyist and 35 points please help asap
The length of the line segment with points (-5, 5) (3, -1) is 10 units
How to find length of lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points (-5, 5) and (3, -1) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-5 - 3)² + (5 - -1)²}
d =√{64 + 36}
d = √100
d = 10 units
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A rectangle has an area of 50 square
centimeters. The width is 5 more than 1 times
the length. Find the length and width, in
centimeters, of the rectangle.
Show your work here
The measurements of the rectangle are 10 cm and 5cm.
What is rectangle?
A rectangle could be a quadrilateral with four right angles in geometer geometry. It may be outlined as an angulate quadrilateral as a result of all of its angles square measure equal; or a quadrangle with a right angle.
Main Body:
Let the width be x.
According to question :
width is 5 more than 1 times the length(l), so
length (l) = width -5
Area if rectangle = 50 cm²
Formula for area of rectangle = length * width
⇒50 = x*(x-5)
⇒50 = x² - 5x
⇒x² - 5x - 50 =0
splitting the middle term
⇒x²- 10x +5x -50 = 0
⇒x(x-10) +5(x-10)
⇒(x-10)(x+5)
Hence the value for x = 10 or -5 .
but length can never be -ve so x= 10.
Width = 10 cm
length = width -5
length = 10 -5
l = 5cm
Hence Measurements of rectangle are 10cm and 5cm.
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Here is an equation: 5x - 5 = 5x + ___. What could you write in the blank so the equation would be true for:
1. No values of x.
2. All values of x.
3. One value of x.
Answer:
1 ; -5 ; 2x
Step-by-step explanation:
1. We must have 0x equal to a number that is not 0
example = 1
5x - 5x = 5 + 1
0 = 6 (false)
2 we must have 0 = 0
-5
5x - 5x = 5 - 5
0 = 0
3 the x must stay
example = 2x
5x - 5 = 5x + 2x
2x = -5
2/2 x = -5/2
x = -5/2
How do you write 5 11/16 and 7 24/25 as a decimal?
Answer:
5 11/16 as a decimal = 5.6875
7 24/25 as a decimal is 7.96
Step-by-step explanation:
Answer:
5 11/16 = 5.6875
7 24/25 = 7.97
Step-by-step explanation:
you keep the whole numbers then you turn the fractions into decimals so to do that you divide 100 by the denominator and whatever the answer is you multiply it by the numerator to get your answer, 100 divided by 16 is 6.25 and 6.25 multiplied by 11 is 68.75 but since the 5 is already the whole number you basically just forget the decimal in 68.75 ( I hope that makes sense)
And for 7 24/25 you do 100 divided by 25 and that’s 4 so now you multiply 24 by 4 and that’s 96 so that goes after the decimal so it’s 7.96 (I hope that helped and all made sense.)