Answer: Width = 7 inches, Length = 14 inches
Step-by-step explanation:
Let the width be [tex]w[/tex]. Then, the length is [tex]2w[/tex].
Using the formula for the perimeter of a rectangle,
[tex]2(w+2w)=42\\\\w+2w=21\\\\3w=21\\\\w=7\\\\\implies 2w=14[/tex]
3z + 6(z-5) = -48
What does this equal please help
Answer: z=-2
Step-by-step explanation:
3z+6z-30=-48
9z-30=-48
9z-30=-48+30
9z=-18
z=-2
air is pumped into a spherical balloon at the constant rate of 200 cubic centimeters per second. how fast is the surface area of the balloon changing when the radius is 5 centimeters?
The rate of change of the surface area of the balloon is 32cm²/sec
We know that volume of the sphere is,
V = 4/3πr³
Given,
dV / dt = +200
r = 5cm
d(SA) / dt = ?
dV / dt = 4πr² dr/dt
80 = 4π (25) dr/dt
dr / dt = 0.8 / π
SA = 4πr²
d(SA) / dt = 8πr dr / dt
d(SA) / dt = 8π × 5 × 0.8 / π
d(SA) / dt = 32cm²/sec
Hence the rate of change of the surface area is 32cm²/sec
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The Coast Guard cutter Angelica travels at 30 knots from its home port of Corpus Christi on a course of 95 degrees for 2 hrs and then changes to a course of 185 degrees for 2 hrs. Find the distance and the bearing from the Corpus Christi port to the boat.
The distance and bearing of the boat from the port areas follows;
The boat is locates at approximately 157.15 kilometers and on a bearing of 150° from the port.
What is a bearing in mathematics?A bearing in mathematics is an angle that is measured clockwise, from the north or y-axis direction.
The speed at which the Coast Guard cutter travels = 30 knots
Bearing of the Coast Guard cutter Angelica = 95°
The time the coast guard travels in the initial direction = 2 hours
The direction the Coast Guard cutter changes to = 185°
Time of traveling in the new direction = 2 hours
30 knots = 55.56 km/hr
The distance traveled in the first direction = 55.56 km/hr × 2 hr = 111.12 km
The distance traveled in the second direction = 55.56 km/hr × 2 hr = 111.12 km
From the attached drawing, we have that the figure formed by the path of the Coast Guard cutter is an isosceles triangle
The distance from the port to the location of the boat, given by Pythagorean theorem is; l = √(111.12² + 111.12²) ≈ 157.15
The distance f the boat from the port is approximately 157.15 kilometers
The base angles of an isosceles right triangle are 45°
Therefore, the bearing is 95° + 45° = 150°
The bearing from the port to the boat is 150°
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a basket contains 13 apples, of which two are rotten. a sample of three apples is selected at random. in how many ways can two rotten apples be chosen? a) 165 b) 11 c) 121 d) 220 e) 9 f) none of the above.
Answer:
None of the above
Step-by-step explanation:
Please help now !!!!!!
Answer:
The tablet costs more than the smartphone
Step-by-step explanation:
1 year tablet = $1.50
1 year smartphone = $0.02x12months = $0.24
How many triangles are in the figure below?
- 5
- 6
- 7 < answer
- 8
This question isn't possible, so I missed it and checked afterwards. Here's the answer for anyone else who may cross it's path. If possible, I'd love to know why 7 is the answer. I really have no idea.
Answer:
7 is correct.
There are 4 small triangles, 2 medium-sized triangles, and 1 large triangle.
if a fair die is rolled, what is the probability of landing on an even number or a number greater than 2
The probability of landing on an even number or a number greater than two is 5/6.
A fair die is rolled. We need to find out the probability of landing on an even number or a number greater than two.
Let the event of landing on an even number be denoted by the variable E1. Let the event of landing on a number greater than two be denoted by the variable E2. We need to calculate P(E1 ∪ E2).
P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)
P(E1 ∪ E2) = (3/6) + (4/6) - (2/6)
P(E1 ∪ E2) = 5/6
Hence, the probability of landing on an even number or a number greater than two is 5/6.
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A researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. Her data is expressed in the scatter plot and line of best fit below. What does the slope of the line represent?
Temperature (Degrees Fahrenheit)
Chirps Per Minute
How long the cricket continues to chirp.
The expected change in number of cricket chirps in one minute for each additional degree Fahrenheit.
The expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.
The expected temperature when the cricket chirps 1 time.
The slope of the line of best fit represents: the expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.
What is a line of best fit?A line of best fit simply refers to a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between data points.
What is a slope?A slope is also referred to as the rate of change and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or data points.
In this scenario, the slope for the given data is the change in temperature with respect to a unit change in the number of chirps sold.
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What is the slope of a line that is parallel to the line y = x 2?
Which expression is equivalent to 4f^2
e
/
1
4f
Answer:
4f^2/3 divided 1/4f 16f^3/3 f/3 3/16f^3 3/f
✓ Lets use algebra and simplify:[tex]\frac{\frac{4f^{2}}{3}}{\frac{1}{4f}} \\=\frac{4f^{2}}{3}* \frac{4f}{1} \\=…
Find a polynomial function of least degree having only real
coefficients, a leading coefficient of 1, and zeros of 4 and
3 + i.
The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
Given,
In the question:
A leading coefficient of 1, and zeros of 4 and 3 + i.
To find the polynomial function of least degree having only real coefficients.
Now, According to the question;
The function has 4 and 3 + i .
As, i's roots
So, 3 - i is also its root a leading coefficient of 1 .
So, The function of polynomial is :
f(x) = (x - 4) [tex][(x - 3)^2 + 1][/tex]
To solve the function;
f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
Hence, The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
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Lines AB and CD (if shown) are straight lines. Find x .
Answer:
x = 20
Step-by-step explanation:
We know that a straight line is 180 degrees. We also know that the line A and B is a supplementary angle.
We subtract 180 - 110 which will come out to 70 which is the value of angle B
We know that angles D and E are 90 degrees and since D and C is 180 degrees, that means C and E is equal to 90 degrees as well.
Since B is equal to 70 degrees, we subtract 90 - 70 to get 20 degrees which is the value of x
Kylie just accepted a job at a new company where she will make an annual salary of $67000. Kylie was told that for each year she stays with the company, she will be given a salary raise of $3000. How much would Kylie make as a salary after 3 years working for the company? What would be her salary after t years?
The amount that Kylie make as a salary after 3 years working for the company is $76000.
Her salary after t years will be 67000 + 3000t.
How to calculate the value?In this situation, Kylie was told that for each year she stays with the company, she will be given a salary raise of $3000 every years.
Her salary after three years will be:
= $67000 + ($3000 × 3)
= $67000 + $9000
= $76000
Her salary after t years will be:
= 67000 + (3000 × t)
= 67000 + 3000t
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the coded values for a measure of brightness in paper (light reflectivity), prepared by two different processes, are as shown in the accompanying table for samples of size 9 drawn randomly from each of the two processes. do the data present sufficient evidence to indicate a difference in locations of brightness measurements for the two processes? give the attained significance level.
The level can be attained by light reflections.
What are light reflections?The law of reflection states that objects can either be observed through the light they emit or, more frequently, through the light they reflect. The law of reflection, which states that the angle of incidence and reflection must be equal, is observed by reflected light.The transition known as reflection flips a shape in a mirror line, also known as a line of reflection, such that each point is at the same distance from the mirror line as its reflected point.n mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflectionlearn more about reflections here:
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A sample of size 50 from a normal distribution has sample mean 5 and sample variance 20. Find 96% confidence intervals for the variance and standard deviation of the distribution.
The standard deviation and variance of the distribution's 96% confidence intervals are 9.841 and 5.704, respectively.
A normal distribution sample of size 50 has an expected higher rate of 20 and a sample mean of 5.
n = 50 makes up the sample size.
Furthermore, the sample variance is s² = 20
The following is the formula for both the variance confidence interval:
σ² = [tex](\frac{(n-1)s^2}{X^2_{{n-1};{1-\alpha /2}}}, \frac{(n-1)s^2}{X^2_{{n-1};{\alpha/2}}})[/tex]
Here, [tex]{X^2_{{n-1};{1-\alpha /2}}}[/tex] is the critical value at the status of significance [tex]\alpha[/tex] & degree of freedom n - 1.
The 90% confidence interval's lower bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (30.114)
= 32.54
The 90% confidence interval's upper bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (10.117)
= 96.86
Consequently, the confidence level for the distribution's variance is (96.86, 32.54).
Additionally, the range of the distribution's standard deviation inside the 90% confidence interval is (√96.86, √32.54), that's the same as (9.841, 5.704).
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As the value of c increase toward infinity, what happens to the values of g(x) = 3x - 19
I got angle D but I am confused with others I need help ASAP tysm
Considering the figure the unknown angles are
a = 65b = 25c = 25How to determine the unknown anglesUsing the angle in a straight line are supplementary we have
60 + a + 55 = 180
a + 115 = 180
a = 180 - 115
a = 65
applying sum of angles in a triangle equal to 180, b is calculated as follows
a + b + 90 = 180 right angle triangle
substituting for a
65 + b + 90 = 180
b + 155 = 180
b = 180 - 155
b = 25
applying vertical angle theorem
angle c = angle b
angle c = 25
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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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Joh rent a kayak at a nearby tate park. He pay a fee of 12. 99 plu 3. 75 for each hour that he pend in the water. How much did Joh pend if he wa on the river 4 1/2 hour
The total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.
Given, Joh rent a kayak at a nearby state park.
He pay a fee of 12.99 plus 3. 75 for each hour that he spend in the water.
We have to find the amount he spend when he was in the water for 4(1/2) hours.
Total amount = 12.99 + hourly amount
Hourly amount = 3.75×4(1/2)
Hourly amount = 3.75×9/2
Hourly amount = 16.875
Total amount = 12.99 + 16.875
Total amount = 29.865
Hence, the total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.
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Step up an inequality for this situation below. Define your variable, but do not solve. (2 points – 1 defined variable, 1 point correct inequality).
Mr. Bass charges his music students $25 per lesson plus a recital fee of $50. How many lessons can a student take if they pay no more than $175?
The lessons can a student take if they pay no more than $175 is 25x + 50 < 175.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
In the 12U Softball division, Olivia gets chosen. What is Olivia's age? Olivia's age is unknown to you because the word "equals" is missing. However, since you are aware that she should be under or equal to 12, you can write Olivia's Age 12. This is a real-world example of an inequality.
given:
Per lesson charges= $25
Recital f= $50
Total money can be spend= $175
let the number of lessons taken be x.
So, the inequality is
25x + 50 < 175
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The image of the point (9, -3)(9,−3) under a translation is (4, 1)(4,1). Find the coordinates of the image of the point (0, 2)(0,2) under the same translation.
pLS HURRY!!!This area model shows the quotient of 1/5+4
What is the quotient?
Enter your answer as a fraction in simplest from by
filling in the boxes.
The quotient of the fraction is 0.05 and the fraction in its simplest form is 1/20
How find the quotient of a fraction?The quotient of a fraction is the whole number that is obtained when you simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction
Given: 1/5÷4
1/5÷4 = 1/5 × 1/4 (Note: If ÷ change to ×, 4 will change to 1/4 )
= 1/20 = 0.05
Therefore, the quotient of the fraction is 0.05 and 1/20 should be filled in the box
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Select the correct answer. Which statement is true about this equation? 3(-y + 7) = 3(y + 5) + 6 A. The equation has one solution, y = 0. B. The equation has one solution, y = -1. C. The equation has no solution. D. The equation has infinitely many solutions.
The statement which is true about this equation is that: C. The equation has no solution.
What is no solution?In Mathematics, no solution is sometimes referred to as zero solution. Additionally, an equation is considered as having no solution when the right hand side and left hand side of the equation are not the same or equal.
This ultimately implies that, an equation would have no solution or zero solution when both sides of the equal sign are not the same and the variables cancel out.
From the information provided above, we have this equation:
3(-y + 7) = 3(y + 5) + 6
Opening the bracket, we have the following:
-3y + 21 = 3y + 15 + 6
Next, we would rearrange the equation by collecting like terms as follows:
-3y + 21 = 3y + 21 (no solution)
-3y - 3y = 21 - 21
-6y = 0
y = -0/6
y = 0
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Mrs. Magdalino kept records on how much she spent on gasoline and the maintenance of her car. She found that it cost $485 to drive 500 mi in a month Find the cost per mileWrite an equation that relates the cost for gasoline and maintenance of a car to the number of miles m the car is driven. Use the equation to find the cost for driving 1200 miles. About how many miles are driven for a cost of $820?
Answer:
C = 0.97m$1164 for 1200 miles845 miles for $820Step-by-step explanation:
Given a car's cost of operation is $485 for 500 miles, you want an equation relating cost for m miles, and solutions to that equation for 1200 miles, and for a cost of $820.
Cost per mileThe cost per mile is found by dividing the cost by the associated number of miles:
$485/(500 mi) = $0.97 /mi
EquationThe equation for the cost will show the cost as the cost per mile multiplied by the number of miles:
C = 0.97m . . . . . where C is cost in dollars for m miles driven
1200 milesThe cost for driving $1200 miles will be ...
C = 0.97(1200) = $1164
The cost of driving 1200 miles is $1164.
$820The number of miles that can be driven for a cost of $820 is ...
820 = 0.97m
m = 820/0.97 = 845.36
About 845 miles are driven for a cost of $820.
13. In the figure, PSR is a straight line. Find RSQ and PQS.
The angle RSQ = 105° and angle PQS = 78°
Given,
In the question:
In the figure,
PSR is a straight line .
To find the angle RSQ and angle PQS.
Now, According to the question;
In ΔQRS,
we know that :
Sum of angle of triangle is 180 degree.
Angle (SQR + QRS + RSQ) = 180°
In the figure,
Angle (23° + 52° + RSQ) = 180°
75° + ∠RSQ = 180°
∠RSQ = 180 - 75
∠RSQ = 105°
We have to find the ∠PQS
Now, PSR is a straight line
In Triangle PSQ
Find the ∠S
105 + ∠S = 180° (Linear Pair)
∠S = 75°
In ΔPQS
Angle(SPQ + PQS + QSP) = 180°
Angle(27° + PQS + 75° ) = 180°
∠PQS = 180 - 102
∠PQS = ∠78°
Hence, The angle RSQ = 105° and angle PQS = 78°
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In a pack of Skittles, 20% are red. If 13 are red, how many skittles were in the entire bag?
The total number of skittles in the bag will be 65.
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 In a pack of Skittles, 20% are red. If 13 are red. The total number of skittles will be calculated as,
N = ( 13 / 20 ) x 100
N = 130 / 2
N = 65
Therefore, the total number of skittles in the bag will be 65.
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IM GIVING BRAINLY I NEED HELP ASAPP
Answer:
C
Step-by-step explanation:
Rate change = Change in Y/ Change in Xy=mx+cand for graph, rate change is 10(10 units change in Y for every 1 unit change in X) whereas another function's rate change is 4
C= is y-intercept
and in graph its -6 whereas in function its -8, so graph has higher y-intercept
Graph: Rate of change = 10, y-intercept = -6
Function: Rate of change = 10, y-intercept = -8
There are 4 consecutive even integers that add up to 4. What is the value of the least integer?
The value of the least integer is -1/2 or -0.5.
How to calculate the value?Based on the information given, let the integers be represented as:
x
x + 1
x + 2
x + 3
Since they all add to 4, this will be:
x + x + 1 + x + 2 + x + 3 = 4
4x + 6 = 4
Collect like terms
4x = 4 - 6
4x = -2
Divide
x = -2 / 4
x = - 1/2
Therefore, the least is - 1/2
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Justify each of the following manipulations to multiply two binomials by filling in the blanks with the associative property the commutative property or the distribution (3x+5)(2x+7)=2x(3x+5)+7(3x+5) helpppp!!
The property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
In this question we have been given an expression.
We need to identify the property that is used to multiply two binomials.
(3x+5)(2x+7)=2x(3x+5)+7(3x+5)
Consider two binomials,
(3x+5)(2x+7)
= (2x+7)(3x+5) ...............(commutative property)
= 2x(3x+5)+7(3x+5) ................(distributive property)
Therefore, the property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
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the number of defectives in 10 different samples of 50 observations each is the following: 5, 1, 1, 2, 3, 3, 1, 4, 2, 3. what is the estimate of the population proportion of defectives?
The estimate of the population proportion of defectives is 0.05.
Given that,
There are 10 different samples of 50 observations, that is, total of 500 observations.
To find : The estimate of the population proportion of defectives
And total number of defectives from 500 observations is (5+1+1+2+3+3+1+4+2+3) = 25
Thus, the point estimate for the population proportion defectives will be,
=25/500=0.05
or just obtain the individual proportion of each sample and then take their average to obtain the same result.
Thus, the point estimate for the population proportion defectives will be 0.05
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