If Neil uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend , then the number of 41 cent stamp used is 3 and number of 6 cent stamps used is 12 .
Let number of 41 cents stamps used be = x ;
and let number of 6 cents stamps used be = y ;
converting amount 41-cents in dollars is = $0.41 ;
and converting amount 6-cents in dollars is = $0.06 ;
the amount for which Neil used 41-cent stamps , 6-cent stamps is = $1.95 ;
this situation in equation form is written as ⇒ 0.41x + 0.06y = 1.95
Multiplying on both sides by 100 , we get
⇒ 41x + 6y = 195 ;
⇒ y = (195 - 41x)/6 ;
We will test this equations for values of x and y , the number of stamps must be whole numbers .
If x = 1 , then value of y is = 25.66
If x = 2 , then value of y is = 18.833
If x = 3 , then value of y is = 12
If x = 4 , then value of y is = 5.166 .
the only value of x and y which shows a whole number as an output is : If x = 3 , then y = 12 .
Therefore , Neil used "3" 41-cents stamps and "12" 6-cent stamps .
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What is the distance between points (4, 36) and (13, -4) on a coordinate plane?
Which the correct solution of the equation 1/2a + 2/3b = 50, when b=30
According to the given formula, the value of a is:
60
If b=30 then 1/2a+2/3b=50
How do you find the value of a in the given equation?First, replace the 30 in b.
1/2a+2/3(30)=50
According to the order of operations, we must first multiply 2/3 by 30. yes:
2/3 times 30 is equal to 20.
2/3 times 30/1. 3 is 10 times 30, so 2 times 10 = 20. Now it looks like this:
1/2a+20=50
20 and 50 are similar terms, so I'll put those two together. Move the positive 20 to the other side where the 50 is. 20 has moved to the other side, so it changes sign and becomes negative.
yes:
1/2a=50-20
50-20 = 30
1/2a=30
Multiply each side by 2, because only 2 makes the variable 1a.
1/2a × 2 = 1a
30 times 2 = 60, so:
1a=60, which is also a=60. So a perfect simplification is a= 60
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Due to the installation of a muffler, the noise level of an engine decreased from 88 to 72 decibels. Find the percent decrease in the intensity of the noise as a result of the installation of the muffler given the following information:
The number of decibels [tex]\beta[/tex] of a sound with an intensity of [tex]I[/tex] watts per square meter is given by [tex]\beta = 10\log\left(\dfrac{I}{I_0}\right)[/tex].
[tex]I_0[/tex] is an intensity of [tex]10^{-12}[/tex] watts per square meter, corresponding roughly to the faintest sound that can be heard by the human ear.
Answer:
97.5% decrease
Step-by-step explanation:
You want the percentage change in noise intensity when it is reduced from 88 to 72 dB.
Intensity ratioThe intensity can be found by solving the given equation for I:
[tex]\beta_1=10\log\left(\dfrac{I_1}{I_0}\right)\\\\10^{\beta_1/10}=\dfrac{I_1}{I_0}\\\\I_1=I_0\cdot10^{\beta_1/10}[/tex]
Similarly, the reduced intensity is ...
[tex]I_2=I_0\cdot10^{\beta_2/10}[/tex]
Percent changeThe percentage change is found from ...
percentage change = (I₂/I₁ -1) × 100%
Using the above expressions for I₁ and I₂, this becomes ...
[tex]\text{\% change}=\left(\dfrac{I_0\cdot10^{\beta_2/10}}{I_0\cdot10^{\beta_1/10}}-1\right)\times100\%\\\\=(10^{(\beta_2-\beta_1)/10}-1)\times100\%=(10^{(72-88)/10}-1)\times100\%\\\\=(10^{-1.6}-1)\times100\% \approx -0.975\times100\% =\boxed{ -97.5\%}[/tex]
The noise intensity decreased by about 97.5%.
__
Additional comment
It can be useful to remember that log(2) ≈ 0.30103. That is, a reduction of 3 dB is a reduction by a factor of 2. Hence 16 db is a factor of about 40.
Answer:
97.49% (2 d.p.)
Step-by-step explanation:
Given equation:
[tex]\beta=10 \log\left(\dfrac{I}{I_0}\right)[/tex]
Divide both sides by 10:
[tex]\implies \dfrac{\beta}{10}= \log\left(\dfrac{I}{I_0}\right)[/tex]
Switch sides:
[tex]\implies \log\left(\dfrac{I}{I_0}\right)=\dfrac{\beta}{10}[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 10^{\frac{\beta}{10}}=\dfrac{I}{I_0}[/tex]
Multiply both sides by I₀:
[tex]\implies I=I_010^{\frac{\beta}{10}}\\[/tex]
Substitute the given value of I₀:
[tex]\implies I=10^{-12} \cdot 10^{\frac{\beta}{10}}\\[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies I=10^{\left(\frac{\beta}{10}-12\right)}\\[/tex]
Therefore, the value of I when β = 88 dB is:
[tex]\implies I=10^{\left(\frac{88}{10}-12\right)}\\[/tex]
[tex]\implies I=10^{-3.2}[/tex]
And the value of I when β = 72 dB is:
[tex]\implies I=10^{\left(\frac{72}{10}-12\right)}\\[/tex]
[tex]\implies I=10^{-4.8}[/tex]
Percent Decrease formula
[tex]\sf Percent\:decrease=\dfrac{original\:value-new\:value}{original\:value} \times 100[/tex]
Therefore, the percent decrease is:
[tex]\implies \dfrac{10^{-3.2}-10^{-4.8}}{10^{-3.2}} \times 100[/tex]
[tex]\implies 97.4881135...\%[/tex]
[tex]\implies 97.49\%\; \sf (2\; d.p.)[/tex]
the variable whose value depends on the input
i need it nowwwww i have 10 mins
Answer:
A dependent variable represents a quantity whose value depends on how the independent variable is manipulated. y is often the variable used to represent the dependent variable in an equation.
Step-by-step explanation:
If FG = 2x, GH = x + 4, and FH = 10, what is FG?
The value for the line segment FG represented by the algebraic expression 2x is equal to 4.
What is an algebraic equationAn algebraic equation is a mathematical statement that contains two equated algebraic expressions.
The sum of the line segments FG and GH is equal to FH so;
2x + x + 4 = 10
3x + 4 = 10
3x = 10 - 4 {subtract 4 from both sides}
3x = 6
x = 6/3
x = 2
line segment FG = 2(2) = 4
line segment GH = 2 + 4 = 6
Therefore, the value for the line segment FG represented by the algebraic expression 2x is equal to 4.
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Convert 1.2% to a decimal
Answer: I think its .012
hope this helps
Answer:
0.012
Step-by-step explanation:
A rectangular piece of metal is 9 in. longer than it is wide, Squares with sides 4 in. long are cut from the four corners, and the flaps are folded upward to form an open box. Which equation indicates that the volume of the box is 56 in.³?
Choose the correct answer below.
OA (x+1)(x-8)=56
OB. x(x +9)(4)=56
OC. (x+1)(x-8)(4)=56
OD. x(x +9)=56
OC (x+1)(x-8)(4)=56 indicates that the volume of the box is 56 in³ because it takes into account the length of the sides after the four corners were cut off, and the height of the box which is 4 in. The equation can be written as (length of sides)(width of sides)(height) = volume.
What is a volume?A volume is a three-dimensional space that contains a specific amount of material, which is commonly measured in liters, cubic meters, or gallons. It is frequently used to calculate the capacity of containers like tanks, bottles, and barrels. Volume may also refer to the quantity of space occupied by an item, such as the volume of a room or the volume of a sphere.
In the given question, OC is the correct answer: (x+1)(x-8)(4)=56. This equation reveals that the volume of the box is 56 [tex]in^{3}[/tex] because it considers the length of the sides after the four corners were taken off, which are (x+1) and (x-8), as well as the height of the box, which is 4 in. The formula is (length of sides)(width of sides)(height) Equals volume. As a result, the equation (x+1)(x-8)(4) = 56 reveals that the box's volume is 56 [tex]in^{3}[/tex].
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A high school class conducts a survey where students are asked about their eye color and whether or not they wear glasses. The two-way table below shows the results of the survey as relative frequencies.
based on the results of the survey, what is the possibility, rounded to the nearest tenth, that a students eye color is brown given that the student wears glasses?
A ) 33.3%
B ) 42.9%
C ) 60.0%
D ) 50.0%
According to the information in the graph, it can be inferred that the percentage of students who have brown eyes among the group that wears glasses is equivalent to 42.9% (option B).
How to calculate the percentage of students who have brown eyes in the group that wears glasses?To calculate the percentage of students who have brown eyes in the group that wears glasses we must perform the following mathematical operation.
We must add all the values of the group that wears glasses
0.04 + 0.08 + 0.12 + 0.04 = 0.280.28 = 100%0.12 = X= 42.85%According to the previous operation, the result must be approximated to 42.9% and the correct option would be B.
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Drag the values to the correct location in the equation. Not all values will be used.
Which two values will make the equation true, for y≠0?
The two values which will make the given equation true are 17 and 4.
By using different processes, simplification refers to reducing the expression to a simpler form. The equation is simplified to its closest value using approximation, which is not perfectly accurate.
Simplification for the given equation:
Consider the given equation and substitute the values 17 and 4 in the blank space.
= 17y∛6y - 14∛48y⁴
= 17y∛6y - 14∛6 × 6y³y
= 17y∛6y - 14 × 2y∛6 × 2³y³y
Further simplifying,
= 17y∛6y - 14 × 2y∛6y
= 17y∛6y - 28∛6y
= - 11∛6y
Therefore, the values for which the 17y∛6y - 14∛48y⁴ = - 11∛6y are 17 and 4.
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caitlyn needs to mail a usb drive to a friend. she uses 40-cent stamps and 7-cent stamps to pay $1.76 in postage. how many of each stamp did caitlyn use?
He used five 40-cent stamps and eight 7-cent stamps.
Let x stand for how many 40-cent stamps he applied.
Let y stand in for the quantity of 7-cent stamps he applied.
41 cents = 40/100 = $0.40
7 cents = 7/100 = $0.07
To cover the $2.56 in postage, he uses 40-cent and 7-cent stamps. That implies
0.4x + 0.07y = 2.56
When you multiply something by 100, you get
40x + 7y = 256
7y = 256 -40x
The accompanying x and y values must both be whole numbers in order to satisfy the equation.
If x = 4,
7y = 256 - 40 × 4 = 96
y = 96/7 = 13.71
If x = 5,
7y = 256 - 40 × 5 = 56
y = 56/7 = 8
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3, 18, 18, 5, 2, 17, 30, 9, 38, 17, 12
Key: 30 = 30
Here is the stem and leaf plot:
Stem Leaf
0 2, 3, 5, 9
1 2, 7, 7,, 8, 8
2
3 0, 8
What is a stem and leaf plot?A stem-and-leaf plot is a table that is used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf.
The stem is the first number in the digit. In this question, the stem is the tens digit. The leaf is the last number. In this question, the leaf is the units digit. For example in the number 18, 1 would be the stem and 8 would be the leaf.
Here is the complete question:
Create a stem and plot diagram using the dataset provided: 3, 18, 18, 5, 2, 17, 30, 9, 38, 17, 12
Key: 30 = 30
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Find the measure of the indicated angle.
The measure of the indicated angle is 33 degrees
How to determine the value of the angleIt is important to note the properties of a triangle
The properties of a triangle are given as;
A triangle has three sides and also three anglesThe sum of the angles in a triangle is 180 degreesThe sum of the exterior angles of a triangle always add up to 360 degreesThe sum of consecutive interior and exterior angle of a triangle is supplementary, that is, they sum up to 180 degreesFrom the diagram shown, we have;
57° + K + 90° = 180°
Collect like terms, we get;
K = 180° - 147°
Subtract the numbers
K = 33°
Hence, the value is 33°
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The tread of a tire is the part that contacts
the road. Find the surface area of the tread
of a tire with a diameter of 32 inches. Round
your answer to the tenths place.
Answer:
That is correct. The probability of rolling a 2 and a 5 when rolling two dice is 1 in 36, which is considered likely.
Answer:
not enough information
Step-by-step explanation:
The tire is shaped like a cylinder. The tread of a tire is the lateral surface of a cylinder. We know the diameter of the cylinder, 32 inches, but we are not given the width of the tire which is the height of the cylinder, so we cannot calculate the area.
Answer: not enough information
Which is the approximate measure of angle yzx? 34.8° 39.4° 50.6° 55.2°
The approximate measure of angle YZX is 39.4°. Option(B) is the correct answer.
we know that
In the right triangle XYZ
[tex]tan(Y Z X)= \frac{opposite side angle YZX}{adjacent side angle YZX}[/tex]
In this problem,
Opposite side angle YZX= XY = 12.4cm
Adjacent side angle YZX= YZ = 15.1cm
substitute the values,
[tex]tan ( Y Z X) = \frac{12.4}{15.1}[/tex]
[tex]Angle ( Y Z X) = arc tan( \frac{12.4}{15.1} )[/tex]
Angle ( Y Z X) = 39.4°
So, the approximate measure of angle YZX is 39.4°.
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The complete question is:
In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?
A .34.8°
B .39.4°
C .50.6°
D. 55.2°
Which of the following ratios are equivalent to 6:9? Choose all that apply.
3:2
18/27
30:45
24/32
Answer:
3:2
Step-by-step explanation:
Point B has coordinates (2,1). The x-coordinate of point A is −3. The distance between point A and point B is 13 units. What are the possible coordinates of point A
Use this diagram to solve questions 8 through 10.
Households
Firms
Financial
intermediaries
T-G
The government
G
What is G when C = 500, S = 200, T = 200, 1 = 300, and Y = 900?
G =
Answer here
A short-run economic event like a recession is more likely to have aggregate demand rather than aggregate supply as its main cause.
What is Keynesian Theory?The theory used in this question is the Keynesian Theory of Income and Expenditure,
It asserts that total spending (C + I + G + X - M) equals total output (Y), where C represents consumption, I represents investment, G represents government spending, X represents exports, and M represents imports.
Step 1: In order to solve for G, we must first recall the equation for calculating Gross Domestic Product (GDP):
GDP = C + I + G + (X - M)
Step 2: We have five of the six variables given in the equation and can solve for G by rearranging the equation to solve for G.
GDP - C - I - (X - M) = G
Step 3: Substitute the given values for each of the variables in the rearranged equation, starting with GDP.
900 - 500 - 300 - (200 - 200) = G
Step 4: To simplify the problem, subtract 500 from each side.
400 - 300 = G
Step 5: 300 should be subtracted from each side of the equation.
100 = G
Therefore, Government spending G = 100.
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a boxcar lot of ball bearings has an average diameter of 2.503 centimeters (cm). this is within the specifications for acceptance of the lot by the purchaser. the inspector happens to inspect 100 bearings from the lot with an average diameter of 2.515 cm. this is outside the specified limits, so the lot is mistakenly rejected. what is the value of the statistic?
The statistic is the average diameter of 100 bearings from the lot, which is 2.515 cm. This is outside the specified limits, resulting in the lot being mistakenly rejected.
The statistic in this case is the average diameter of the inspected bearings from the lot. The lot contains a boxcar of ball bearings, and the specified acceptance of the lot is that the average diameter must be 2.503 cm. The inspector happens to inspect 100 bearings from the lot and determines that the average diameter of these bearings is 2.515 cm, which is outside the specified limits. As a result, the lot is mistakenly rejected. The value of the statistic is the average diameter of the inspected bearings from the lot, which is 2.515 cm. This is the value that determined the lot's rejection, as it is outside the specified limits.
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Rocky has 7 bottles of water. he will buy more bottles of water from the store. the store has 8 cases in stock and each case contains 24 bottles of water. the store will not sell partial cases. the function that models the number of bottles of water rocky will have after his purchase is , where c is the number of cases of water he buys. what is the practical domain of the function?
Answer:
{1, 2, 3, 4, 5, 6, 7, 8}
Step-by-step explanation:
In this problem, we use the variable c to represent the independent quantity. This means that the domain is all possible values for c. Since the store only has 8 cases of water, the domain cannot be any number larger than 8. Since the store only sells complete cases, not partial cases, of water, the domain cannot be a fraction or decimal number. This means that the practical domain, or domain that makes sense for the problem situation, is {1, 2, 3, 4, 5, 6, 7, 8}.
Please only answer problem number 44 from the picture. fill-in-the-blanks using each of the numbers 027 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest. Justify your answer.
By using each of the numbers 0 - 7 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest are,
⇒ 20.3% , 4.56, and 9/1
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.
Here, We have to use each of the numbers 0 - 7 exactly once.
Hence, The percent, decimal, in fraction below are ordered from least to greatest are,
⇒ 20.3% = 0.203
⇒ 4.56
⇒ 9/1 = 9
Thus, By using each of the numbers 0 - 7 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest are,
⇒ 20.3% , 4.56, and 9/1
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HELP ME ASAPPPPP please make it right because i’m in so much trouble rn.
Desi has a coupon that entitles him to 35% off the regular price of a sweater. The original price of the sweater he would like to buy can be represented as x , so Desi says that the price he will pay is (1−0. 35)x. Write another expression that represents the price Desi will pay
If Desi has a coupon that entitles him to 35% off the regular price of a sweater , then another expression that represents the price Desi will pay is 0.65x .
the original price of the sweater is = x ;
the percent discount that Desi gets by applying the coupon is = 35% ;
Desi gets 35% discount , it means that Desi only need to pay the remaining 65% of the price .
So , the remaining price of the sweater to be paid by Desi is = 65% of "x" ;
= 0.65x ...(because 65% = 0.65 ) .
Therefore , the another expression representing the situation is 0.65x .
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write the standard form of the euation of the line through the given point with the given 15) through: (3,3) slope = -1/2
The standard form of the equation of the line through the point (3,3) with slope -1/2 is y = -1/2x + 9/2.
The standard form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
We are given a point (3,3) and a slope of -1/2, we can use the point-slope form to write the equation of the line as follows -
y - 3 = -1/2(x - 3)
To convert this equation to standard form, we can simplify the equation as follows -
y - 3 = -1/2x + 3/2
y = -1/2x + 3 + 3/2
y = -1/2x + 9/2
Hence, the standard form of the equation of the line through the point (3,3) with slope -1/2 is y = -1/2x + 9/2.
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Find the balance in the account after the given period. $7,700 deposit earning 3.9% compounded monthly, after 4 years.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7700\\ r=rate\to 3.9\%\to \frac{3.9}{100}\dotfill &0.039\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 7700\left(1+\frac{0.039}{12}\right)^{12\cdot 4}\implies A=7700(1.00325)^{48} \implies A \approx 8997.69[/tex]
Rewrite x4y2 − 2x3y3 using a common factor.
Answer:
x²y²(x²-2xy)
Step-by-step explanation:
they each include an x²y² so you take out the x²y² from each, and then write what's remaining & then add a bracket.
What is the perimeter of 6(1/2x + 5)
Answer: The perimeter of a rectangle is the sum of the lengths of all four sides. If one of the sides is 6(1/2x + 5), then we can find the perimeter by multiplying that by 2.
Perimeter = 2*6(1/2x + 5)
Perimeter = 12(1/2x + 5)
To simplify the expression, we can distribute the 12:
Perimeter = 121/2x + 125
Perimeter = 6x + 60
So the perimeter of 6(1/2x + 5) is 6x + 60.
Step-by-step explanation:
Lila knows that 3/16 means ""3 divided by 16. "" She uses this to find the decimal equivalent for 316
Lila finds out the decimal equivalent of 3 divided by 16 is equal to 0.1875.
Lila knows that 3/16 means "3 divided by 16."
To find the decimal equivalent for 3/16, she would divide 3 by 16 using a calculator or long division. This would give her a decimal answer of 0.1875.
It's important to note that 3/16 is a fraction, which represents a ratio of two numbers, the numerator, and the denominator. The decimal equivalent is simply another way to represent the same value but in decimal form.
Lila understands that to convert fractions to decimals, she can divide the numerator by the denominator. And to convert decimals to fractions, she can write the decimal as a fraction with the denominator as a power of 10.
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Students plan to decorate the school's flagpole with strings of lights. One end of each string of lights will be attached
to the top of the flagpole, and the other end will be attached to the ground.
String
of lights
-Flagpole
String
of lights
15 ft
- 8 ft + 8 ft
Which measurement is closest to the length of one string of lights in feet?
The length of one string of lights in feet is closest to 23 feet.
The problem states that students plan to decorate the school's flagpole with strings of lights. One end of each string of lights will be attached to the top of the flagpole, and the other end will be attached to the ground.
The flagpole is 15 feet tall and the distance from the base of the flagpole to the ground is 8 feet. Since the string of lights is attached at the top of the flagpole and at the ground, the length of the string of lights is equal to the height of the flagpole plus the distance from the base of the flagpole to the ground.
Therefore, the length of one string of lights can be calculated by adding the height of the flagpole (15 feet) to the distance from the base of the flagpole to the ground (8 feet), which results in:
15 feet + 8 feet = 23 feet
So the length of one string of lights is 23 feet.
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Ali runs each lap in minutes. He will run at least minutes today. What are the possible numbers of laps he will run today? Use for the number of laps he will run today. Write your answer as an inequality solved for .
The possible minutes Ali will run today can be represented by the inequality x ≥ 66.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given that,
Minutes taken to complete one lap = 6 minutes
Also, he will run at least 11 laps today.
This means that Ali will run laps greater than or equal to 11 laps.
Let x be the number of minutes taken by Ali today.
x ≥ 6 × 11
x ≥ 66
Hence Ali runs 11 laps in at least 66 minutes.
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The complete question is as follows :
Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today?
4 Brooke cycled at an average speed of 22 kilometers per hour from her house to the nearby park,
and cycled back at an average speed of 14 kilometers per hour vio the same route. She took
66 minutes to cycle back to her house. How long, in minutes, did she take to ode from her house
to the nearby park?
The time taken to cover the distance from the park to house with an average speed of 22km /h is 42 minutes.
What is average speed?Average speed is the directional speed of an object in motion as measured by a certain unit of time and seen from a particular point of reference. Average speed is a fundamental concept in kinematics, the branch of classical mechanics that investigates how bodies move.
Since average speed is a physical vector quantity, its magnitude and direction must be included in the definition. In the SI, speed is a coherent derived unit whose quantity is measured in metres per second (m/s), where speed is the scalar absolute value (distance) of average speed (metric system). The word "acceleration" describes a change in an object's speed, direction, or both.
we know that
distance = average speed × time
distance = 14×66/60 =15.4 km
now time = distance /average speed
time = 15.4×60/ 22 = 42 minutes
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