Step-by-step explanation:
x, y = 2 numbers
x = 2y
y - x/2 = 20
this is impossible to solve. there is no solution.
because the first equation tells us
y = x/2
and so the second equation is
x/2 - x/2 = 20
0 = 20
so, again, no solution.
How do I do C?Someone please help asap.
You have to find the slope of the line. It will give you the conversion rate from inches to centimetres or the other way around.
Looking closely at the graph, or using a ruler as reference, you can estimate that 30 cm ≈ 12 in. In terms of the graph, the line very nearly passes through the point (12, 30). It also passes through the origin, (0, 0), since 0 cm = 0 in exactly.
The slope of the line is then
[tex]\dfrac{30\,\mathrm{cm}-0\,\mathrm{cm}}{12\,\mathrm{in}-0\,\mathrm{in}} = \dfrac{30\,\rm cm}{12\,\rm in} = \dfrac{5\,\rm cm}{2\,\rm in} = 2.5\dfrac{\rm cm}{\rm in}[/tex]
which means that 1 in ≈ 2.5 cm.
So, if Sarah's height is 64 in, we convert this to cm and find her height is (approximately)
[tex]64\,\mathrm{in} \times 2.5\dfrac{\rm cm}{\rm in} = \boxed{160\,\rm cm}[/tex]
John noticed that the angle formed by the minute hand and hour hand on a standard 12-hour clock was 110 degrees when he left home after 6 p.m.; it was also 110 degrees when he returned before 7 p.m. that same night. If he left home for more than five minutes, for how many minutes was he away
Jhon was between 6:12 p.m and 6:52 p.m. So, Jhon left home for exact 40 minutes. Using the angle made by the hands in the clock, the required value is calculated.
How to find the angle between the minute hand and hour hand?The general formula for finding the angle between the minute hand and the hour hand is
M = [tex]\frac{2}{11}[/tex] (H × 30 ± θ)
Calculation:It is given that,
Jhon left home after 6 p.m with an angle of 110° formed by the minute hand and hour hand.
So,
M = [tex]\frac{2}{11}[/tex] (H × 30 - θ)
= [tex]\frac{2}{11}[/tex] (6 × 30 - 110)
= [tex]\frac{2}{11}[/tex] (180 - 110)
= [tex]\frac{2}{11}[/tex] × 70
= 140/11
So, he left after 6:12 p.m
Jhon returned home before 7 p.m with angle of 110° formed by the minute hand and hour hand.
M = [tex]\frac{2}{11}[/tex] (H × 30 + θ)
= [tex]\frac{2}{11}[/tex] (6 × 30 + 110)
= [tex]\frac{2}{11}[/tex] (180 + 110)
= [tex]\frac{2}{11}[/tex] × 290
= 580/11
So, he returned before 6:52 p.m
Then,
The time taken for returning home = 580/11 - 140/11 = 440/11 = 40 minutes.
Therefore, he took 40 minutes to return home.
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A rectangular paperboard measuring 20 invhes long and 15 inches wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer.)
The perimeter of the rectangle is 70 Inches square
How to determine the perimeterThe formula for perimeter of a rectangle is given as;
Perimeter = 2 ( l + w)
length = 20 inches
width = 15 inches
Perimeter = 2 ( 20 + 15 )
Perimeter = 2 ( 35)
Perimeter = 70 Inches square
Thus, the perimeter of the rectangle is 70 Inches square
Note that it is a general knowledge on the given question.
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pls help :,)
What is the area of this triangle?
units²
Answer:
6 [tex]units^{2}[/tex]
Step-by-step explanation:
The formula for the area of a triangle is A = [tex]\frac{1}{2} bh[/tex]. The base in this case is the length of DE, 4 - 1 = 3 units. The height of this triangle is 1 + 3 = 4 units.
A = [tex]\frac{1}{2} bh[/tex] = [tex]\frac{1}{2} *3*4[/tex] = 6
8. A company has 350 workers. The
president of the company wants to know
what percent increase in employment
would be necessary for the number of
workers to be greater than 375.
Help!
The percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%
How to determine the rates?The given parameters are:
Initial = 350
Final = 375
The rate is calculated as:
Rate = Final/Initial - 1
So, we have:
Rate = 375/300 - 1
Evaluate
Rate = 1.25 - 1
This gives
Rate = 0.25
Express as percentage
Rate = 25%
Hence, the percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%
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Identify the solutions to the quadratic equation 6x^2+x-1=0
Answer:
1/3 and -1/2
Step-by-step explanation:
You can use the factoring method to identify the solutions of x
6x^2+x-1
2 numbers have to multiply to 6 and subtract to 1 because x is the same as 1x
So, you get 3x and 2x
since you know that -1x1 is -1 you will get
(3x-1)(2x+1)=0
Now, since (3x-1) and (2x+1) multiply to get 0, if either (3x-1) or (2x+1) is 0 the statement will be valid
3(1/3)-1=0
2(-1/2)+1=0
So, your answers are 1/3 and -1/2
The factorization of x² + 3x -4 is modeled with algebra
tiles.
+X
+
+
+
+
+X
+X
+X
+X
+X
+X
Ť
T
What are the factors of x² + 3x - 4?
O(x + 4) and (x-4)
O(x + 3) and (x-4)
(x + 4) and (x-1)
O(x+3) and (x-1)
Option C
Each of the following is an example of quantitative data, except Group of answer choices weight in ounces income in dollars political affiliation age in years
The correct option is C. political affiliation.
An example of quantitative data are-
weight in ouncesage in yearsincome in dollarsWhat is quantitative data?Data that expresses a definite quantity, amount, or range is known as quantitative data. In most cases, the data is accompanied with measuring units, such as metres in the case of a person's height. Setting boundaries for such data makes sense, and performing mathematical operations on the data has significance.
Types of Quantitative Data are-
Counter: A measure of entities. For instance, the quantity of users who have downloaded a specific app from the App Store.Measurement of physical objects: Calculating the dimensions of any physical object is called measurement. The HR executive, for instance, meticulously measures the size of each cubicle given to the new hires.Sensory calculation: Mechanism to automatically "sense" the parameters being monitored in order to generate a continuous source of data. A digital camera, for instance, transforms electromagnetic signals into a string of numerical data.Data projection: Algorithms and other mathematical analysis techniques can be used to project future data. For instance, after conducting a thorough investigation, a marketer will forecast a rise in sales following the introduction of a new product.To know more about quantitative data, here
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The complete question is-
8. Each of the following is an example of quantitative data, except ______.
A. weight in ounces
B. income in dollars
C. political affiliation
D. age in years
The graph of f(x) = 1/3
is reflected vertically, compressed horizontally by a factor of 5, shifted
right 2 units and down 6 units. Write the equation of the new graph.
The transformed function is defined by:
g(x) = -f(x/5 - 2) - 6
Where f(x) is the given function.
How to get the equation of the transformed function?Here we start with the function:
f(x) = (1/3)*x
(I don't know if this is the actual function, but that does not matter, I will solve it in a general way).
If first, we reflect it vertically, then the new function is:
g(x) = -f(x).
If now we compress it horizontally by a factor of 5, then we get:
g(x) = - f(x/5)
Now we shift it 2 units to the right, then:
g(x) = -f(x/5 - 2)
Finally, we shift it down 6 units, then we get:
g(x) = -f(x/5 - 2) - 6
That is the general form of the function g(x).
Replacing f(x) by what is defined above, we get:
g(x) = -(1/3)*(x/5 - 2) - 6
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The spinner of the compass is two congruent isosceles triangles connected by their bases as shown in the diagram. The base of each of these triangles is 2 centimeters and the legs are 5 centimeters.
2 congruent isosceles triangles are connected by their bases. A circle is drawn around the triangles.
If the metal used to construct the spinner costs $13.25 per square centimeter, how much will it cost to make this part of the compass? Round to the nearest cent.
Cost = $
Applying the area of a rectangle, the cost to make the part of the compass is: $129.85.
What is the Area of a Triangle?Area of a triangle = 1/2(base)(height).
Find the height of the triangle using the Pythagorean theorem:
Height = √(5² - 1²) ≈ 4.9 cm.
Base = 2 cm
Area of the two triangles = 2[1/2(base)(height)]
Area of the two triangles = 2[1/2(2)(4.9)] = 9.8 cm².
Cost to to make this part of the compass = 9.8 × $13.25 = $129.85.
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Answer: 129.82
Step-by-step explanation: its on edge I got it right :)
an equation for loudness, in decibles, is L=10log10 R where R is the relative intensity of the sound. Sounds that reach levels of 120 decibles or more are painful to humans what is the relative intensity of 120 decibles
Considering the logarithmic loudness equation, the relative intensity of 120 decibels is of [tex]R = 10^{12}[/tex].
What is the logarithmic loudness equation?The equation is:
[tex]L = 10\log{R}[/tex]
In which:
L is the loudness, in decibels.R is the relative intensity.For this problem, we have that L = 120, hence the relative intensity is found as follows:
[tex]120 = 10\log{R}[/tex]
[tex]\log{R} = 12[/tex]
[tex]R = 10^{12}[/tex]
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In a right triangle, the length of the hypotenuse is 12 and the measure of one of the angles is 36. What is the length of the other leg
Answer:
Either 9.71 (adjacent to 36°) or 7.05 (opposite 36°)
Step-by-step explanation:
The question doesn't specify which leg is under question. Is it the adacent leg or the opposite leg? I'll assume adjacent.
We can use the acronym
SOHCAHTOA which is a helpful mnemonic for remembering the definitions of the trigonometric functions. For an angle other than the right angle, the following relationships are defined.
SOH: S is sine = Opposite/Hypotenuse
CAH: C is cosine = Adjacent/Hypotenuse
TOA: T is tangent = Opposite/Adjacent
For a side adjacent (A) to the 36° angle, we can use
Cosine = Adjacent/Hypotenuse
Since we know the hypotenuse (12) we can find A:
Cosine(36) = A/12
A = Cosine(36)*12
A = (0.809)*12
Adjacent = 9.71
====================
If the opposite leg is calculated, we would use
Sine= Opposite/Hypotenuse
Sine(36) = Opposite/12
O = (0.5877)*12
Opposite = 7.053
If the polynomials p(x) = ax³+4x²+3x-4 and q(x) = x² - 4x + a, leave the same remainder when divided by (x-3), find value of a.
Steps pls
Answer:
a = -22/13.
Step-by-step explanation:
By the Remainder Theorem
p(3) = remainder when p(x) is divided by x-3.
q(3) is equal to the same remainder.
So we have:
p(3) = q(3) , so
a(3)^3 + 4(3)^2 + 3(3) - 4 = 3^2 - 4(3) + a
27a + 36 + 9 - 4 = 9 - 12 + a
27a - a = 9 - 12 - 36 - 9 + 4
26a = -12 - 36 + 4
26a = -44
a = -44/26
a = -22/13.
find the value of k.
(x^2+5x+k)/(x+6) has a remainder of 9.
if anyone could help, please do!! this is urgent!
The value of k in the polynomial is 3
How to solve for k?The quotient is given as:
(x^2+5x+k)/(x+6)
The remainder is 9
Set the denominator to 0
x + 6 = 0
Solve for x
x = -6
This means that:
f(-6) = 9
So, we have:
(-6)^2 + 5(-6) + k = 9
Evaluate
6+ k = 9
Subtract 6 from both sides
k = 3
hence, the value of k is 3
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Which expression is equivalent to startroot 8 x superscript 7 baseline y superscript 8 baseline endroot? assume x greater-than-or-equal-to 0.
Expression which is equivalent to [tex]$\sqrt{8 x^{7} y^{8}}[/tex] is [tex]$=2 \sqrt{2} x^{3} y^{4} \sqrt{x}$[/tex].
What are equivalent expressions?
Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).
Solution of the given equation [tex]$\sqrt{8 x^{7} y^{8}}[/tex].
[tex]$\sqrt{8 x^{7} y^{8}}=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]
[tex]$=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]
Simplify [tex]$\sqrt{x^{7}}: x^{3} \sqrt{x}$[/tex]
[tex]$=\sqrt{8} x^{3} \sqrt{x} \sqrt{y^{8}}$[/tex]
Simplify [tex]$\sqrt{y^{8}}: y^{4}$[/tex]
[tex]$=\sqrt{8} x^{3} \sqrt{x} y^{4}$[/tex]
[tex]$\sqrt{8}=2 \sqrt{2}$[/tex]
[tex]$=2 \sqrt{2} x^{3} \sqrt{x} y^{4}$[/tex]
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The complete question is :
Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0. x y squared StartRoot 8 x cubed EndRoot 2 x cubed y cubed StartRoot x y squared EndRoot 2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot 4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
35 POINTS please help asap
Type the correct answer in each box. Use numerals instead of words.
This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?
f(x) = _x(x - _)
f(x) = _(x − _)^2 + _
i know for sure the first four blanks are 2, 4, 2, and 2 but the last is NOT 8.
The quadratic equation given in the graph can be represented in these two following ways:
Factored: f(x) = 2x(x - 4).Vertex form: y = 2(x - 2)² - 8.What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this graph, the roots are [tex]x_1 = 0, x_2 = 4[/tex], hence the factored form of the polynomial is:
f(x) = ax(x - 4).
When x = 5, y = 10, hence the leading coefficient is found as follows:
10 = 5a(5 - 4)
5a = 10
a = 2.
Hence the factored form of the polynomial is:
f(x) = 2x(x - 4).
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the vertex is at point (2,-8), hence h = 2, k = -8 and:
y = a(x - 2)² - 8
When x = 5, y = 10, hence the leading coefficient is found as follows:
10 = a(5 - 2)² - 8
9a = 18
a = 2.
Hence the equation in vertex-form is:
y = 2(x - 2)² - 8
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Gavin collects a certain type of seashell. He has 160 seashells. The seashells' weights are distributed normally with a mean of 120 grams and a
standard deviation of 26 grams.
How many of the seashells weigh at least 68 grams?
A 109
B. 156
C. 134
D. 152
Answer:
Answer: B.156
Step-by-step explanation:
Given: Total seashells = 160
mean = 120
population standard deviation = 26 grams
The probability that the seashells weigh at least 68 grams :-'
Total seashells weigh at least 68 grams = 0.9772 x 160 = 156.352≈ 156
Hence, the correct option is B.156
please mark brainiestThe function f(x) = 200 × (1.098)x represents a village's population while it is growing at the rate of 9.8% per year.
Create a table to show the village's population at 0, 2, 4, 6, 8, and 10 years from now.
Use your table to create a graph that represents the village's population growth.
When the population doubles from its current size, the village will need to dig a new water well. To the nearest half of a year, about how long before it is time for the village to dig the new well?
The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.
How to graph a function?For a function f(x) = y, the steps to draw a graph for the given function are as follows:
Consider certain values of x Substitute x values in the given function to obtain y valuesPlot the x and y values in the graphJoin the points to know the variation.Calculation:It is given that,
f(x) = 200 × [tex](1.098)^x[/tex]
Village's population growing rate = 9.8%
Creating a table for x and f(x) values:
x: 0 2 4 6 8 10
f(x = 0) = f(0) = 200 × [tex](1.098)^0[/tex] = 200
f(x = 2) = f(2) = 200 × [tex](1.098)^2[/tex] = 241
f(x = 4) = f(4) = 200 × [tex](1.098)^4[/tex] = 291
f(x = 6) = f(6) = 200 × [tex](1.098)^6[/tex] = 350
f(x = 8) = f(8) = 200 × [tex](1.098)^8[/tex] = 423
f(x = 10) = f(10) = 200 × [tex](1.098)^1^0[/tex] = 509
So,
(x, f(x)): (0, 200) (2, 241) (4, 291) (6, 350) (8, 423) (10, 509)
Plotting these points in the graph and joining the points, the graph is shown below.
Finding the time for the village to dig a new well:
It is given that the population doubled from its current size, the village will need to dig new water well.
The current size of the village = 200
If it doubles for a certain time 't' = 400
So,
400 = 200 × [tex](1.098)^t[/tex]
⇒ [tex](1.098)^t[/tex] = 2
⇒ log[tex](1.098)^t[/tex] = log 2
⇒ t log(1.098) = 0.301
⇒ t × 0.04 = 0.301
∴ t = 7.525 years
Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.
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A 14 oz bag of flour costs $2.95 and a 28 oz bag of flour costs $6.20. What is the price per ounce of the 14 oz bag of flour?
The price per ounce of the 14 Oz bag of flour is; ¢21.1.
What is the price per ounce of the 14 oz bag of flour?Since it follows from the task content that the 14 Oz bag of flour sells for $2.95 which is equivalent to ¢295 since $1 = ¢100.
It follows that the price per ounce of the 14oz bag of flour is; = ¢295/14 = ¢21.1
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There are 20 red and blue marbles in a bag. s marbles are red how many are blue?
Answer:
Step-by-step explanation:
Step-by-step explanation:
15 r blue marbles
20- 5 = 15
In convex pentagon $ABCDE$, angles $A$, $B$ and $C$ are congruent and angles $D$ and $E$ are congruent. If the measure of angle $A$ is 40 degrees less than the measure of angle $D$, what is the measure of angle $D$
The measure of angle D in the convex pentagon ABCDE is 132°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the measure of angle D, hence:
angle A = x - 40.
∠A + ∠B + ∠C + ∠D + ∠E = 540° (sum of angle in a pentagon)
3(x - 40) + 2x = 540
x = 132°
The measure of angle D in the convex pentagon ABCDE is 132°
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Given: ΔABC is a right triangle and CD ⊥ AB.
Prove: AC2 + BC2 = AB2
Which reason completes the proof?
A.
Corresponding sides of similar triangles are proportional.
B.
Corresponding parts of congruent triangles are congruent.
C.
Corresponding parts of similar triangles are congruent.
D.
Corresponding sides of congruent triangles are proportional.
Answer:
Corresponding parts of similar triangles are congruent.
Step-by-step explanation:
Joel spends 272727 more minutes playing soccer after school on Tuesday than he did on Monday. He still exercises for a total of 606060 minutes after school.
What percent of his time exercising after school did Joel spend playing soccer on Tuesday?
Joel spent 72.5% of his time exercising after playing soccer on Tuesda
How to determine the percentage?The given parameters are
Minutes spent on Tuesday = 27 more minutes than Monday
Total minutes spend = 60
This means that
Tuesday = Monday + 27
Monday + Tuesday = 60
Make Monday the subject in Tuesday = Monday + 27
Monday = Tuesday - 27
Substitute Monday = Tuesday - 27 in Monday + Tuesday = 60
Tuesday - 27 + Tuesday = 60
Evaluate
2 * Tuesday = 87
Divide by 2
Tuesday = 43.5
The percentage of time spent exercising on Tuesday is then calculated as
Percentage = 43.5/60 * 100%
Evaluate the expression
Percentage = 72.5%
Hence, Joel spent 72.5% of his time exercising after playing soccer on Tuesday
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when evaluating (6.28x10^12)\(3.14x10^4)
Answer:??? rest of the question I think is what will be the exponent of 10 in the quotient? answer is 8
Step-by-step explanation:
A new car is purchased for $45, 000 and over time its value depreciates by one half
every 3.5 years. What is the value of the car 17 years after it was purchased, to the
nearest hundred dollars?
For what values of o is tan o undefined?
Answer:
90 is the right answer
Step-by-step explanation:
because it give the value pf o is tan o
Time Remaining
55:45
Circles C and D overlap. The distance from point C to point D is 7 centimeters.
What is the sum of the areas of circle C and circle D?
7Pi units squared
14Pi units squared
49Pi units squared
98Pi units squared
The sum of the areas of circle C and circle D is 98 units square. Option D
How to determine the areaIt is important to note that the if the circles overlap each other, then the most have the same radius
Also, the formula for area of a circle is given as;
Area = [tex]\pi r^2[/tex]
For Circle C
The value for π = 3. 142
radius = 7cm
Substitute the values into the formula
We have
Area = π × 7 × 7
Area = 49 π units square
For Circle D
Substitute the values into the formula
Area = [tex]\pi r^2[/tex]
Area = π × 7 × 7
Area = 49 π units square
Sum of the areas of circle C and circle D = area of circle C and area of circle D
Sum of the areas of circle C and D = 49π + 49 π
= 98 units square
The sum of the areas of the circles is 98 units square
Thus, the sum of the areas of circle C and circle D is 98 units square. Option D
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A university wants to determine the average salary of its graduating computer science majors. the university asks the graduating classes of 50 students to share their starting salaries when hired. the 50 students had an average salary of $100,000 with a standard deviation of $2,000. find a 95% confidence interval for the average starting salary of computer science majors from the university.
Option B. ($99,242.00, $100,758.01)
a) For n - 1 = 49 degrees of freedom, we have form t distribution tables:
P( t < 2.010) = 0.975
Therefore, P(-2.010 < t < 2.010) = 0.95
Therefore the confidence interval here is obtained as:
X +₋ t 8/√ⁿ
100 \pm 2.010*\frac{2}{\sqrt{50}}
100 \pm 0.5685
(99431.61, 100568.39)
Therefore A is the correct interval here.
Q2) From t distribution tables, we have here:
P(-2.680 < t < 2.680) = 0.99
Therefore the confidence interval here is obtained as:
100 \pm 2.010*\frac{2}{\sqrt{50}}
100 \pm 0.7580
(99242, 100785)
1) A university wants to determine the average salary of its graduating computer science majors. The university asks the graduating classes of 50 students to share their starting salaries when hired. The 50 students had an average salary of $100,000 with a standard deviation of $2,000. Find a 95% confidence interval for the average starting salary of computer science majors from the university.
a - ($99,431.61, $100,568.39)
b - ($99,445.64, $100,554.36)
c- ($99,982.26, $100,017.74)
d - The salaries are not normally distributed so we cannot compute a confidence interval
2) Find a 99% confidence interval for the previous problem.
a - ($99,271.44, $100,728.56)
b - ($99,242.00, $100,758.01)
c - ($99,996.46, $100,003.55)
d - The salaries are not normally distributed so we cannot compute a confidence interval
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hi can you please help me
Answer:
See attached image
Step-by-step explanation:
I'm uncertain as to the "best statement." None seem to accurately describe the situation. I picked the one that was least incorrect (if that makes any sense).
The counting numbers beginning with 101 and ending with 200 are listed. How many of the numbers have a 6 as a digit
Counting numbers from 101 to 200, those with 6 as a digit are 19
The numbers
Let's start by listing all the number between 101 and 200
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
Now, let's count the numbers with 6 as a digit
= 19 numbers has 6 as a digit
Thus, counting numbers from 101 to 200, those with 6 as a digit are 19
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