Joel needs 1.5 gallons of blue paint.
Joel needs a total of 10 gallons of paint to paint the outside of his house. Since the ratio is 3 parts blue paint to 2 parts yellow paint, we can use proportions to solve for the amount of blue paint needed.
We can set up the proportion like this:
3/2 = x/10
We can solve for x (the amount of blue paint) by cross-multiplying:
3*10 = 2*x
3*10 = 20x
20x = 30
x = 30/20
x = 1.5
Joel needs 1.5 gallons of blue paint.
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Perform the indicated operations.
a^2-4 ,,,,,,,,a^2-2a ,,,,,,,,2-y
--------- ÷ ------------- + ---------
x^2-9 ,,,,,,,,, xy+3y,,,,,,,,, x-3
PS. (------ is to show a fraction)
Awnser = [ ] IF X does not equal something
Answer: (a^2 - 4)/(x^2 - 9) + (a^2 - 2a + (2-y))/(xy + 3y) - (x-3)
Step-by-step explanation: First, you need to simplify the fraction in the first term:
(a^2 - 4)/(x^2 - 9)
Next, you simplify the fraction in the second term:
(a^2 - 2a + (2-y))/(xy + 3y)
Then you subtract (x-3) from the fractions obtained in step 1 and 2:
(a^2 - 4)/(x^2 - 9) + (a^2 - 2a + (2-y))/(xy + 3y) - (x-3)
This is the final result of the operation.
It is important to note that the answer is a simplified fraction and only valid if x does not equal 3. If x=3, the denominator x-3 would be equal to zero, which is not allowed in mathematics.
A local pizza shop has a membership program for frequent buyers. The membership
costs $20 per month and members get a discounted price of $2 per slice of pizza.
Alang purchased a membership to this pizza shop. How much would Alang have to
pay the pizza shop if he bought 17 slices of pizza this month? What would be the
monthly cost for a slices of pizza?
Answer:
$32
$22
Step-by-step explanation:
We know
Membership cost per month = $20
Price of a slice of pizza for members = $2
How much would Alang have to pay the pizza shop if he bought 17 slices of pizza this month?
The total cost of Alang on 17 slices of pizza = membership cost per month + prices of 17 discounted pizza
$20 + $2(6) = $32
What would be the monthly cost for a slice of pizza
The monthly cost of Alang a slice of pizza = membership cost per month + price of 1 discounted pizza
$20 + 2 = $22
So,
Alang would have to pay $32 if he bought 17 slices of pizza this month.
The cost of a slice of pizza is $22
Can someone help me solve this?
[tex]f(t)=0.4(1.16)^{t-1}\qquad \begin{cases} x=0.4\\ y=1.16 \end{cases}\implies f(t)=xy^{t-1} \\\\[-0.35em] ~\dotfill\\\\ xy^{t-1}\implies xy^t y^{-1}\implies x\cfrac{y^t}{y}\implies \cfrac{x}{y}y^t\implies \stackrel{\textit{substituting back}}{\cfrac{0.4}{1.16} ~~ (1.16)^t} \\\\\\ \stackrel{\textit{"r" is positive, \Large Growth}}{\cfrac{0.4}{1.16} ~~ (1+0.16)^t \implies f(t)~~ \approx ~~ 0.34 ~~ (1+0.16)^t}\qquad \begin{cases} a\approx 0.34\\\\ r=0.16 \end{cases}[/tex]
Determine if each function is linear or nonlinear. drag each function into a box to correctly classify it. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. linear nonlinear
A: y = 2x³, is a non-linear function.
B: y = x + 5, is a linear function.
C: y = x² − 3, is a non-linear function.
D: 5x + 5y = 25 and y = x² / 2, is a linear and non-linear function.
What is a function?
A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
If the degree of the function is one. Then the function will be a linear function.
If the degree of the function is not one. Then the function will be a non-linear function.
Hence,
A: y = 2x³, is a non-linear function.
B: y = x + 5, is a linear function.
C: y = x² − 3, is a non-linear function.
D: 5x + 5y = 25 and y = x² / 2, is a linear and non-linear function.
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A: y = 2x³, is a non-linear function.
B: y = x + 5, is a linear function.
C: y = x² − 3, is a non-linear function.
D: 5x + 5y = 25 and y = x² / 2, is a linear and non-linear function.
A statement, idea, or rule that creates a link between two variables is known as a function. Mathematics has functions, which are necessary for the creation of meaningful connections.
if the function has a degree of one. The function will thereafter be linear in nature.
if the function's degree is not one. The function will then be non-linear in that case.
As a result, the function A: y = 2x3 is not linear.
B: The linear function y = x + 5 is given.
C: The non-linear function y = x2 3 is.
D: The equation 5x + 5y = 25 has a linear and nonlinear component, y = x2 / 2.
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If tanθ = 13 what is the value of 7sin2θ+3cos2θ
I think the question should be tan theta = 1/√3, but I have given the solutions of both.
Hope it helps.
If you have any query, feel free to ask.
find the slope m of the tangent to the curve y = 3/ x at the point where x = a > 0.
The slope m of the tangent to the curve will be m = -3/a^2.
Calculating the slope of the tangent line to the curve y = 3/x at a point where x = a > 0 is an important mathematical concept. To do this, we will first need to find the derivative of the curve y = 3/x.
Let's start by taking a look at the equation for the slope of a line: m = (y2-y1) / (x2-x1). We'll use this equation to find the slope of the tangent line at the point (a, 3/a).
To do this, we'll need to calculate the derivative of the given equation, which is y' = -3/x^2.
At the point (a, 3/a), the derivative is equal to -3/a^2. Therefore, the slope of the tangent line at the point (a, 3/a) is m = -3/a^2.
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WILL MAKE BRAINLIEST! Find the solution to the system of equations. Round to the nearest tenth if necessary.
Answer:
The solution to the system of equations g(x) = x - 1 and f(x) = x^2 - 5 is the point where the two functions intersect, which is the point (1,0).
To confirm this, we can substitute x = 1 into each equation and see that they both equal 0:
g(1) = 1 - 1 = 0
f(1) = 1^2 - 5 = -4 + 1 = -3 = 0
So (1,0) is the solution to the system of equations.
The Scale On A Map Is 1 Inch = 60 Miles. If Two Cities Are 2 3/4 Inches Apart On The Map, How Many Miles Are They Apart?
As you answer the following questions, write explanations for why your current answer is correct
A - 58.3 mi
B - 165 mi
C - 120 mi
D - 21.8 mi
The Scale On A Map Is 1 Inch = 60 Miles. If Two Cities Are 2 3/4 Inches Apart On The Map, the number of miles they are apart is, 165 Miles
So, Option B is correct.
What is the scale factor ?Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.
For example, Two spheres look similar but could have different radii.
Given that,
The Scale On A Map Is 1 Inch = 60 Miles
Two Cities Are 2 3/4 Inches Apart On The Map
The number of miles they are apart =?
1 Inch = 60 Miles
11/4 Inch = 60 × 11/4 Miles
= 165 Miles
So, The actual distance is 165 Miles
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draw a box plot for quiz scores of her class. what are the highest and the lowest quiz score? what is the score that separates the bottom 75% from the top 25%? how many students scored more than the median? how many students scored more than 14 points? what percent of her students received less than 12 points? would the score of 4 be an outlier? (use the iqr method to ex
Therefore , the solution of the given problem of median comes out to be the typical grade received by pupils is 80.
Define median.The median value of an arranged dataset is the precise value that makes up its mean. The ratio between the minimum and maximum 50% of the data is what is known as a likelihood measure, or an average. Based if there is an odd or perhaps an even number of points, multiple formulas are used to calculate the median and mode.
Here,
The range and scatter of statistical data are represented visually by this analysis (continuous data).
It establishes four quartile groups.
Min - 25th Percentile, Quartile Group 1 (Q1)
Group 2 of the Quartile: 25th Percentile (Q1) to 50th Percentile (Q2, Median)
50th percentile (Q2) and 75th percentile make up Quartile Group 3. (Q3)
75th percentile (Q3) for Quartile Group 4: Maximum
Q3-Q1 is the interquartile range in this (IQR)
the 40-point cutoff
a maximum score of 110
25% of the class received a score between 40 and 63.
50% of the pupils got scores under 81, and 50% got scores over 81.
75% of pupils had scores between 40 and 95. additionally, 25% of students achieved 95 or higher.
The typical grade received by pupils is 80.
Therefore , the solution of the given problem of median comes out to be the typical grade received by pupils is 80.
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The complete question is " Professor A. has 40 students in her class. After giving a first quiz, she calculated 5 measures of relative standing: min =3, Q1 = 12, Median = 14, Q3 = 16, Max = 20. Draw a box plot for quiz scores of her class. What are the highest and the lowest quiz score? What is the score that separates the bottom 75% from the top 25%? How many students scored more than the median? How many students scored more than 14 points? What percent of her students received less than 12 points? Would the score of 4 be an outlier? (use the IQR method to explain)"
Complete loss of contact between articulating surfaces. Articular cartilages are damaged, ligaments tear, and the joint capsule is distorted
This is a condition known as ankylosis, and it describes a situation in which two bones lose their contact with each other.
What is ankylosis?Ankylosis can result from a variety of causes, including trauma, infection, or degenerative joint diseases. In cases of trauma, the articulating surfaces of the bones can be damaged, leading to a complete absence of contact between the two bones. Similarly, if an infection is present, the cartilage and ligaments of the joint can be destroyed, leading to ankylosis.
Finally, in cases of degenerative joint diseases, such as arthritis, the joint's articulating surfaces can be damaged, leading to a complete loss of contact between the two bones.
The symptoms of ankylosis vary depending on the severity of the condition. In mild cases, the patient may experience stiffness, pain, and reduced range of motion in the joint. In more severe cases, the joint may become completely immobile, and the patient may have difficulty walking or performing other activities.
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The employees of a manufacturing company pledged the following donations in peso
for the establishment of a community pantry: 100, 400, 250, 50, 200, 300, 100, 50, 150, 250,
500, 100, 300, 50, and 150. Using the employees’ contributions, calculate and interpret the
following:
a.) upper quartile b.) 7th decile c.) 35th percentile
Solution:
50, 50, 50, 100, 100, 100, 150, 150, 200, 250, 250, 300, 300, 400, 500
a. Upper quartile or 3
=
4
( + 1) 3 =
3
4
(15 + 1) =
3
4
(16) =
48
4
= 12
3 is in the 12th position. Therefore, 3 = 300.
b. 7
th decile or 7
=
10
( + 1) 7 =
7
10
(15 + 1) =
7
10
(16) =
112
10
= 11.2
Interpolate: 11.2nd position is between the 11th and 12th position which are 250 and
300, respectively. 300-250=50 then 250+0.2=250.2. Hence, D7=250.2
c. 35th percentile or 35
=
100
( + 1) 35 =
35
100
(15 + 1) =
7
20
(16) =
112
20
= 5.6
Interpolate: 5.6th position is between the 5th and 6th position which are 100 and 100,
respectively. Hence, P35=100.
Guide Questions:
1. How did you determine the value of the upper quartile, 7th decile and the 35th
percentile?
2. How will you interpret the results? PLEASE HELP ME
The value of upper quartile is, 300.
The value of 7th decile is, 250.2.
The value of 35th percentile is, 100.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The donations are as follows,
⇒ 50, 50, 50, 100, 100, 100, 150, 150, 200, 250, 250, 300, 300, 400, 500.
Now, We find the values as;
a) The upper quartile is,
⇒ Qₐ = a/4 (n + 1)
Here, n = 15
So, We get;
⇒ Q₃ = 3/4 (15 + 1)
= 3/4 × 16
= 12
So, Q₃ is in 12th position.
So, The value of Q₃ = 300
The value of 7th decile is,
⇒ D₇ = 7/10 (15 + 1)
= 7/10 × 16
= 11.2
Here, 11.2 is between the position 11th and 12th position which are 250 and 300 respectively.
Then, We get;
⇒ 300 - 250 = 50
Hence, The value of D₇ = 250 + 0.2
= 250.2
Now, The value of 35th percentile is,
⇒ Pₐ = a/100 (n + 1)
⇒ P₃₅ = 35/100 (15 + 1)
= 35/100 × 16
= 5.6
Here, 5.6 is between the 5th and 6th position which are 100 and 200 respectively.
Hence, P₃₅ = 100
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A soccer player has a large cylindrical water cooler that measures 2.5 feet in diameter and is 5 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.
98.13 gallons
733.98 gallons
24.53 gallons
183.49 gallons
The number of gallons that are in the water cooler when it is completely full is; 183.49 gallons
How to find the volume of a cylinder?The formula for the volume of a cylinder is;
V = πr²h
Where;
V is volume
r is radius
h is height
We are given;
Radius(r) = diameter/2 = 2.5/2 = 1.25 ft
Height(h) = 5 ft
Thus;
V = π * 1.25² * 5
V = 24.53125 ft³
There are approximately 7.48 gallons of water in a cubic foot, therefore;
Number of gallons in 24.53125ft³ = (24.53125 * 7.48)/1
Number of gallons = 183.49 gallons
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Answer: 183.49 gallons (D)
Step-by-step explanation:
Okay you are trying to find how many gallons of water the water cooler can hold.
So start by using the formula for the volume of a cylinder.
V = πr^2h
First find the radius, which is half the diameter.
The diameter is 2.5 so divide that by 2 to find the radius.
2.5/2 = 1.25
Now that you know the radius, times it by itself:
1.25 x 1.25 = 1.5625
Now multiply 1.5625 by the height, which is 5.
1.5625 x 5 = 7.8125
Now multiply 7.8125 by 3.14
7.8125 x 3.14 = 24.53125
And finally, multiply 24.53125 by 7.48
24.53125 x 7.48 = 183.49375 gallons
Now round to the nearest hundredth:
183.49 gallons
I did the same test and got it right and I have picture proof that it is correct.
What is meant by absolute term?
The absolute value or modulus |x| of a real number x is the non-negative value of x without regard to its sign.
The absolute value is always a positive value and not a negative number. so those numbers are called absolute values.
It is represented as |a|, which defines the magnitude of any integer ‘a’.
It defines removing any negative sign in front of a number and thinking of all numbers as positive.
Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin (zero point) of a number line or coordinate system.
When x itself is negative (x<0), then its absolute value is necessarily positive
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PLEASE HELP
Determine the rate of change and initial value
The rate of change is -1/2
Initial point is (-2,-1)
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
Consider any two pairs of points:
(-2,-1) and (0,-2)
The slope is the same as the rate of change
Rate of change = change in y values/change in x values
= (-2 - (-1) ) / (0-(-2))
= ( -2 + 1) / (+2)
Rate of change = (-1/2)
The rate of change is -1/2
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Which expression is equivalent to StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot
the expression StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot is equivalent to 25x9y3 / 64x6y11.
StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot
= 25x9y3 / 64x6y11
StartRoot is the beginning of the root expression and StartFraction is the beginning of the fraction within the root expression. 25x9y3 is the numerator of the fraction and 64x6y11 is the denominator of the fraction. Superscript is used to raise the numbers to the power indicated. Baseline is the number which the Superscript is raised to. EndFraction indicates the end of the fraction and EndRoot indicates the end of the root expression.
Therefore, the expression StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot is equivalent to 25x9y3 / 64x6y11.
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Simon decided to develop his own board game and sell it from home, advertising on a social media platform.
His biggest decision is what price to sell the game at. He studies similar games to determine he can use the
function P(z) = -125 (17)2 +25000, where P is total profit and is the retail price, to determine
what price to sell his game.
Answer: Simon can use the function P(z) = -125z^2 + 25000 to determine the total profit he will make at different retail prices for his board game. The function shows that his profit will be maximum at 25000 dollars and it will decrease as the price increases or decreases from that point. Simon can use this function to determine the optimal price to sell his game at in order to maximize his profit.
Step-by-step explanation:
Which of the following is equivalent
To
(3) ი
73)
(7¹0) (38)
B. (7) (3)
C. 16
꿇
3
A.
D.
The expression that is equivalent to the given question is option D. (7^5)/ (3^4)
The law of Indices.Indices is a topic in mathematics which has its applications in performing arithmetic operations on numbers with powers. This process requires some laws; which are referred to as the law of indices. These laws have their various applications as required.
By applying the appropriate law of indices to the given question, the equivalent expression can be determined as;
From the numerator;
(7^2)(7^6)(3^2) = (7^8)(3^2)
So that;
(7^8)(3^2)/ (7^3)(3^6) = (7^(8-3)) (3^(2-6))
= (7^5)(3^-4)
The equivalent expression is;
(7^5)(3^-4) = (7^5)/ (3^4)
The equivalent expression is (7^5)/ (3^4). Thus option D.
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which function could represent the value of an antique vase that decreases over time? type of problem
If the value of an antique vase decreases at a rate of 7% a year , and the price of vase a years ago was $1200 , then the current value of vase is $1116 .
The value of the antique vase a years ago was = $1200 ;
the percent decrease in the value of the antique vase is = 7% ,
So , let the present value of the vase be = $x ;
the present value of the vase ca be calculated as = [tex]1200-7\% \; of 1200[/tex] ;
= [tex]1200-0.07\times 1200[/tex] ;
Simplifying further ,
we get ;
= [tex]1200-84[/tex] ;
= 1116 .
Therefore , the current value of the antique vase is $1116 .
The given question is incomplete , the complete question is
The value of an antique vase decreases at a rate of 7% a year. If the vase was valued at $1200 years ago, what would its current value be?
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Solve for x.
8.7 +X = 7
1.1
X = [?]
Answer:
X = 1.7
Step-by-step explanation:
To solve for x, you can subtract 8.7 from both sides of the equation.
8.7 + X = 7
-8.7 -8.7
X = -1.7
So X = -1.7
[tex]8.7+x=7[/tex]
Rearrange:
[tex]x+8.7=7[/tex]
Subtract 8.7 from both sides:
[tex]x+8.7-8.7=7-8.7[/tex]
[tex]\fbox{x = -1.7}[/tex]
solve the given differential equation by separation of variables. dy/dx = x sqrt 1 − y2
The supplied differential equation by variable separation is y(x) = sin(x²/2+c), as stated in the statement.
Of the following is a numerical technique?Any equation containing one or more terms and first or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f (x) In this case, the variables "x" and "y" are isolated and dependent, respectively. For illustration, dy/dx = 5x. Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.
With respect to that differential equation [tex]\frac{d y}{d x}=x \sqrt{1-y^2}[/tex]
[tex]\frac{d y}{\sqrt{1-y^2}}=x d x[/tex]
By implementing integration across both sides,
[tex]\begin{aligned}& \int \frac{d y}{\sqrt{1-y^2}}=\int x d x \\& \sin ^{-1}(y)=\frac{x^2}{2}+c \quad\left[\int \frac{d y}{\sqrt{a^2-y^2}}=\sin ^{-1}\left(\frac{y}{a}\right)\right]\end{aligned}[/tex]
[tex]y(x)=\sin \left[\frac{x^2}{2}+c\right][/tex]
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Express the shear function in terms of x, where x is in meters, for the beam in (Figure 1). Express your answer in terms of x.
A perpendicular force is applied to a beam. The maximum force is 12 kN. The resulted shear function is S(x) = - 2x²
When a perpendicular force is applied to static material (in this case, a beam), shearing forces occur.
Shearing force is calculated as the algebraic sum of all transverse forces acting on either side of a beam or frame section.
First, look at the ratio between forces (in y-direction) and x.
y/x = 12/3
y = 4x
Let S(x) = shear function.
Applying Newton's first law on y-axis:
∑Fy = 0
S + x · 4x · 1/2 = 0
S + 2x² = 0
S = - 2x²
Therefore, the shear function is S(x) = - 2x²
The figure in your question is missing. Most likely it was like on the attached picture.
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if weshipit offers a flat rate of $7.95 to ship a parcel up to ten pounds (as long as it fits within a 18 cm x 18 cm x 18 cm box), how many cubes can be shipped in this box for $7.95? be sure to check both the size and the weight constraints. ignore the weight of the box.
Cannot be answered because of incomplete data.
It is not possible to determine the number of cubes that can be shipped in this box for $7.95 without more information about the size and weight of the cubes. The weight constraint of ten pounds and the size constraint of 18 cm x 18 cm x 18 cm box only applies to the overall package and not to the individual cubes. The weight and volume of the individual cubes would need to be taken into account in order to determine how many could fit within the package while still adhering to the weight and size constraints.
The correct question should be:
if weshipit offers a flat rate of $7.95 to ship a parcel up to ten pounds (as long as it fits within a 18 cm x 18 cm x 18 cm box), how many cubes can be shipped in this box for $7.95? be sure to check both the size and the weight constraints. ignore the weight of the box. Consider the weight of the cube as 2 grams.
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In one day a certain gadget company produced 5000 phones but of these phones, 100 are dejective. What ration represents the fraction of phones that were not dejective ?
Please I need an answer i don't understand this math problem
slap please explain
Thank you...
Answer:
The amount of phones that were not defective is 98% or 49/50 as a fraction in simplest form
Step-by-step explanation:
Steps to solve "what percent is 100 of 5000?"
100 of 5000 can be written as:
100/5000
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
100
5000
×
100
100
= (
100 × 100
5000
) ×
1
100
=
2
100
Therefore, the answer is 2%
If you are using a calculator, simply enter 100÷5000×100 which will give you 2 as the answer. That lets you know how many were defective
If only 2% were defective, then 98% were not
PLSSSS HELLPPPPPPP
How far is it across the lake?
Answer:
9 km
Step-by-step explanation:
By making use of the tangent function, we can calculate the angle inside the right triangle formed with the Lake and the 6km as two of the sides. See the attached worksheet for the detailed steps.
Can you come up with the equation for the graph to the left in y = mx + b form?
Answer:
hope this helps you to understand.
Find the area of a square garden perimeter is 60m.
Class 6 level
Answer:225 m^2
Step-by-step explanation:
Answer:
A = 225 m²
Step-by-step explanation:
the sides of a square are congruent
the perimeter is the sum of the 4 congruent sides (s) , then
s = 60 ÷ 4 = 15 m
the area (A) of a square is calculated as
A = s² , then
A = 15² = 225 m²
a spherical glass bulb measures 31.5 mm in diameter. what is the volume of the bulb in cubic centimeters?
The volume of the spherical glass bulb is approximately 14.1 cubic cm.
To find the volume of a spherical glass bulb, we can use the formula for the volume of a sphere:
[tex]V = 4/3 * pi * r^3[/tex]
Where V is the volume, pi is a mathematical constant (approximately equal to 3.14), and r is the radius of the sphere.
We know the diameter of the bulb is 31.5mm and to find the radius of the sphere, we divide the diameter by 2.
So, radius (r) = 31.5mm / 2 = 15.75mm
Now we can substitute this value into the formula for the volume of a sphere:
[tex]V = 4/3 * pi * (15.75mm)^3[/tex]
We can convert the value of radius from mm to cm by multiplying it by 10^-3
[tex]V = 4/3 * pi * (15.75 * 10^{-3})^3[/tex]
Now we can calculate the value of V
V ≈ 14.1 cubic cm
Therefore, the volume of the spherical glass bulb is approximately 14.1 cubic cm.
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Let p, q, and r be the propositions p: Grizzly bears have been seen in the area. q: Hiking is safe on the trail. r: Berries are ripe along the trail. Write these propositions using p, q, and r and logical connectives (including negations). (a) Berries are ripe along the trail, but grizzly bears have not been seen in the area. (b) Grizzly bears have not been seen in the area and hiking on the trail is safe, but berries are ripe along the trail. (c) If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area. (d) It is not safe to hike on the trail, but grizzly bears have not been seen in the area and the berries along the trail are ripe. (e) For hiking on the trail to be safe, it is necessary but not sufficient that berries not be ripe along the trail and for grizzly bears not to have been seen in the area. (f) Hiking is not safe on the trail whenever grizzly bears have been seen in the area and berries are ripe along the trail.
The following question can be solved using concepts of mathematical reasoning.
Mathematical reasoning is the process of using logical and systematic thinking to arrive at conclusions and make connections between mathematical concepts. It involves making logical deductions and inferences based on mathematical statements, definitions, postulates, and theorems.
Let p, q, and r be the propositions
p: Grizzly bears have been seen in the area.
q: Hiking is safe on the trail.
r: Berries are ripe along the trail.
a) Berries are ripe along the trail, but grizzly bears have not been seen in the area.
Solution:
r ∧ ~p
b) Grizzly bears have not been seen in the area and hiking on the trail is safe, but berries are ripe along the trail.
Solution:
~p∧q∧r
c) If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area
Solution:
r → (q ↔ ~p)
d) It is not safe to hike on the trail, but grizzly bears have not been seen in the area and the berries along the trail are ripe.
Solution:
~q ∧ ~p ∧ r
e) For hiking on the trail to be safe, it is necessary but not sufficient that berries were not ripe along the trail and for grizzly bears not to have been seen in the area.
Solution:
q → (~r ∧ ~p)
f) Hiking is not safe on the trail whenever grizzly bears have been seen in the area and berries are ripe along the trail.
Solution:
(f) (p ∧ r) → ~q
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Assume the random variable x is normally distributed with mean u = 50 and standard deviation o = 7. Find the indicated probability. P(x >43) P(x>43)= Assume the random variable x is normally distributed with mean u = 81 and standard deviation = 4. Find the indicated probability P(70
The indicated probability P(x >43) of the random variable x normally distributed is 0.8414.
What is Normal Distribution?Abraham de Moivre, a Frenchman, was the first to recognize the normal distribution (1667-1754). The curve was later developed further and its equation was developed by Carl Friedrich Gauss (1777–1855); for this reason, it is also more generally referred to as the "Gauss bell" or "Gaussian distribution."
Any point (x) from a normal distribution can be converted to the standard normal distribution using the formula z = (x-mean) / standard deviation (z).
Given:
Mean u = 50
Standard Deviation o = 7
To find the probability P(x>43),
= [tex]P(\frac{x - 50}{7} > \frac{43 - 50}{7} )[/tex]
= [tex]P(z > -1) = 0.8414[/tex]
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A memberhip to Gym A cot $200 to ign up and $10 per month. Gym B’ memberhip cot $0 to ign up and $60 a month. Write an equation to find out how many month you can belong to each gym for it to cot the ame at both place
So, the equation to determine the number of months is 200 + 10x = 0 + 60x.
Let x be the number of months you can belong to each gym for it to cost the same at both places.
The equation to determine the number of months is:
200 + 10x = 0 + 60x
To solve for x, we can subtract 200 from both sides of the equation:
10x = -200
And finally, we divide both sides by 10:
x = -20
Therefore, you can belong to each gym for -20 months for it to cost the same at both places. But since month are positive numbers, x=-20 is not a solution. Therefore, the statement is not true, the cost will never be the same for both gyms.
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