The ratio x:y in its simplest form is 7:4.
The ratio x:y can be found by dividing x by y. In this case, we can start with the equation y = 4x/7 and solve for x in terms of y.
Multiplying both sides by 7, we get:
7y = 4x
Dividing both sides by 4, we get:
x = 7y/4
Now we can substitute this expression for x into the ratio x:y:
x:y = (7y/4):y
Simplifying by canceling out the y, we get:
x:y = 7/4
So the ratio x:y in its simplest form is 7:4.
This means that for every 7 units of x, there are 4 units of y. The ratio cannot be simplified further because 7 and 4 do not have any common factors other than 1.
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Suppose the events Upper B 1, Upper B 2, and Upper B 3, are mutually exclusive and complementary events, such that P(Upper B 1)equals0. 05, P(Upper B 2)equals0. 4, and P(Upper B 3)equals0. 55. Consider another event A such that P(A|Upper B 1)equals0. 6, P(A|Upper B 2)equals0. 5, and P(A|Upper B 3)equals0. 4. Use Bayes's Rule to find P(Upper B 1|A)
The probability of event Upper B 1 given event A is approximately 0.0134.
To find P(Upper B 1|A) using Bayes' rule, we need to use the formula:
P(Upper B 1|A) = P(A|Upper B 1) × P(Upper B 1) / P(A)
To find P(A), we can use the law of total probability:
P(A) = P(A|Upper B 1) × P(Upper B 1) + P(A|Upper B 2) × P(Upper B 2) + P(A|Upper B 3) × P(Upper B 3)
Substituting the given values, we get:
P(A) = 0.6 × 0.05 + 0.5 × 0.4 + 0.4 × 0.55
P(A) = 0.029 + 0.2 + 0.22
P(A) = 0.449
Now, substituting the values of P(A|Upper B 1), P(Upper B 1), and P(A) into the Bayes' rule formula, we get:
P(Upper B 1|A) = (0.6 × 0.05) / 0.449
P(Upper B 1|A) = 0.006 / 0.449
P(Upper B 1|A) ≈ 0.0134
Therefore, the probability of event Upper B 1 given event A is approximately 0.0134.
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A triangular prism with dimensions 8 inches by 13 inches
by 16 inches in placed in a box of the same dimensions, as
show in the figure below. How many cubic inches of filler
material are required to surround the triangular prism in
order to completely fill the box?
=.
.
104
416
832
1,664
13
Cannot be determined by the given information
8
16
To fully describe a triangular prism, you would need to provide the dimensions of its triangular bases (e.g. base length and height), the length of the prism, and the length and width of the rectangular faces. Thus, option C is correct.
What is the triangular prism with dimensions?To find the volume of filler material required to surround the triangular prism, we need to first calculate the volume of the box and the volume of the triangular prism.
The volume of the box is given by:
[tex]8[/tex] inches × [tex]13[/tex] inches × [tex]16[/tex] inches = [tex]1,664[/tex] cubic inches
The volume of the triangular prism is given by:
[tex](1/2) × 8[/tex] inches × [tex]13[/tex] inches × [tex]16[/tex] inches = [tex]832[/tex] cubic inches
To completely fill the box, we need to add filler material with a volume equal to the difference between the volume of the box and the volume of the triangular prism, which is:
cubic inches— [tex]832[/tex] cubic inches [tex]= 832[/tex] cubic inches
Therefore, the [tex]832[/tex] Cubic inches.
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The 1989 U. S. Open golf tournament was played on the East Course of the Oak Hills Country Club in Rochester, New York. During the second round, four golfers scored a hole in one on the par 3 sixth hole. The odds of a professional golfer making a hole in one are estimated to be 3,708 to 1, so the probability is 1/3,709. There were 175 golfers participating in the second round that day. A. What is the probability that no one gets a hole in one on the sixth hole
The probability that no one gets a hole on the sixth hole is given as follows:
0.9534 = 95.34%.
What is the binomial distribution formula?The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
The mass probability formula is given as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single independent trial of the experiment.The parameter values for this problem are given as follows:
n = 175 -> number of golfers.p = 1/3709.The holes are independent, hence the probability of no one getting a hole in the sixth hole is P(X = 0), thus:
P(X = 0) = (1 - 1/3709)^175
P(X = 0) = 0.9534 = 95.34%.
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The graph shows a two-dimensional side view of a
satellite dish and the small reflector inside it. The vertex
of the small reflector is 6 in. from focus F₁ and 20 in. from
focus F2. What equation best models the small reflector?
Picture of graph attached !!! please help
The equation is -7x+y=0.
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
Hence, The equation is -7x+y=0.
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please show work!!!!!!!
Answer:
J. 56
Step-by-step explanation:
The picture in this question can be a little deceiving. Each rectangular glass pane is 3 by 10 inches. This means that the picture of the 4 panes overlapping, leaves the center square open. The open area has your inner edges. The question asks for the sum of the inner and outer edges.
Every pane is 10 inches long, so the out perimeter of the figure is 40 inches because the figure has four sides. The rectangles overlap, creating 3 by 3 inch square. 3 inches off either side of a pane leaves 4 inches as the length for the edge of the inner square. Therefore, the perimeter of the inner square is 16 inches.
Outer Perimeter + Inner Perimeter = 40 + 16 = 56 inches
Related to your response to Question 5, is the standardized mean
difference in Dexter and Hughes (2011) the unbiased or biased
version?
effect size measure.
In the case of Dexter and Hughes (2011), the standardized mean difference is an unbiased version.What is an unbiased estimate?An unbiased estimate is a statistical term used to describe an estimate or forecast that has an equal chance of being too high or too low. In Dexter and Hughes (2011), the standardized mean difference is unbiased.A study's standardized mean difference is determined by dividing the difference between two means by their pooled standard deviation. It's used to compare two group means and is a standardized effect size measure.
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You need a 30% alcohol solution. On hand, you have a 675 mL of a 5% alcohol mixture. You also have 75% alcohol mixture. How much of the 75% mixture will you need to add to obtain the desired solution?
you will need____mL for the 75% solution
You need to add 225mL of the 75% alcohol solution to obtain the desired 30% alcohol solution.
To find the amount of 75% alcohol solution needed to obtain a 30% alcohol solution, we must use the formula for dilution:
M1V1 = M2V2
Where M1 is the concentration of the initial solution, V1 is the volume of the initial solution, M2 is the desired concentration, and V2 is the desired volume.
In this case, M1 is 5%, V1 is 675mL, M2 is 30%, and V2 is unknown.
We can rearrange the equation to solve for V2, which is the volume of the 75% alcohol solution needed:
V2 = (M1V1) / M2
V2 = (5% x 675mL) / 30%
V2 = 225mL
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A bakery sells apple pies for $12.85. if the pie has a diameter of 10 inches, what is the approximate cost per square inch of the apple pie? round to the nearest hundredth. a. $0.04 b. $0.16 c. $0.32 d. $0.65
The cost per square inch of the apple pie is $ 0.16.
Given that,
The diameter of the pie = 10 in
The radius of the pie = 10/2
= 5 inches.
Area of the pie = [tex]\pi r^{2}[/tex]
= 3.14 × 5²
= 3.14 × 25
= 78.5 in²
The cost of the apple pie = $ 12.85.
Therefore, the cost per square inch of the pie = 12.85 ÷ 78.5
= $ 0.16.
Hence, the cost per square inch of the apple pie is $ 0.16.
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Lara's Burgers cooks its burgers either well done or medium. Last night, the restaurant served 9 well-done burgers and 11 medium burgers. What percentage of the burgers served were well done?
45% of the burgers served were well-done.
What is percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
To find the percentage of well-done burgers, we need to divide the number of well-done burgers by the total number of burgers served and then multiply by 100 to get the percentage.
Total number of burgers served = 9 well-done + 11 medium = 20
Percentage of well-done burgers = (9/20) x 100% = 45%
Therefore, 45% of the burgers served were well-done.
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Please refer to the photo!
Help me find the perimeter please!!
Answer:
[tex]P = 56\sqrt2[/tex]
Step-by-step explanation:
We can find the perimeter of a square given its diagonal by modeling the square as two congruent right triangles and using the Pythagorean Theorem to solve for the square's side lengths.
The Pythagorean Theorem states that...
[tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are the right triangles legs, and [tex]c[/tex] is its hypotenuse.
However, since we are working with a square, we know that the right triangles' legs are congruent. Thus, the theorem becomes:
[tex]a^2 + a^2 = c^2[/tex]
[tex]2 \cdot a^2 = c^2[/tex]
Using this formula, we can solve for the square's side lengths, inputting the given hypotenuse length of 28.
[tex]2 \cdot a^2 = 28^2[/tex]
↓ simplify the exponent
[tex]2 \cdot a^2 = 784[/tex]
↓ divide both sides by 2
[tex]a^2 = 392[/tex]
↓ take the square root of both sides
[tex]a = \sqrt{392}[/tex]
↓ simplify the square root
[tex]a = \sqrt{2^3 \cdot 7^2}[/tex]
[tex]a = (2\cdot 7)\sqrt{2}[/tex]
[tex]a=14\sqrt2[/tex]
Finally, we can multiply the side length by 4 to get the square's perimeter (since a square has 4 sides).
[tex]P = 4 \cdot a[/tex]
[tex]P = 4 \cdot 14\sqrt2[/tex]
[tex]\boxed{P = 56\sqrt2}[/tex]
[tex]\boxed{P \approx 79.2}[/tex]
The mass of a sheet of metal varies jointly with it's area and it's thickness. A sheet of metal of area 250cm and thickness 1mm has a mass of 200g
The mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.
The mass of a sheet of metal is directly related to its area and thickness. This means that the mass of a sheet of metal is proportional to the product of its area and its thickness. Mathematically, this can be expressed as the formula M = kAT, where M is the mass, k is a constant, A is the area and T is the thickness.In the given example of a sheet of metal with an area of 250 cm and a thickness of 1mm, we can calculate the mass of the sheet by substituting the given values into the formula: M = k(250)(1) = 200g. The constant k in this example is equal to 0.8 g/cm*mm.Therefore, the mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.
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What is the mass of a sheet of metal with an area of 250cm and a thickness of 1mm?
I need help on this!
Answer:
He is now selling only one product and making less money because he is not selling other TVs.
Step-by-step explanation:
So if you read the paragraph, you get to the point where he says only making and selling the television model that makes the most money. If you think about it if they only sell one product, the other products they used to sell aren't being sold and they are making less money. I hope this helps!
A. What is the magnitude of an earthquake with amplitude 100,000? How
do you know?
The magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale
What do you mean by Magnitude and amplitude in term of Earthquake ?Magnitude: The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. It is typically determined using a logarithmic scale called the Richter scale or other similar scales like the moment magnitude scale (MMS), surface wave magnitude (Ms), or body wave magnitude (Mb). The Richter scale is based on the amplitude of the largest seismic wave recorded on a seismographs, and each increase of one unit on the scale corresponds to a ten-fold increase in the amplitude of the seismic waves and a 32-fold increase in the amount of energy released.
Amplitude: The amplitude of an earthquake is the size of the seismic waves that are generated by the earthquake. It is measured in microns (millionths of a meter) and is recorded on a seismographs. The amplitude of seismic waves can vary greatly depending on the distance from the earthquake's epicenter and the geological structure of the surrounding area.
The magnitude of an earthquake is a measure of the amount of energy released during the earthquake, and is typically determined using a logarithmic scale called the Richter scale.
The formula for calculating the magnitude of an earthquake based on its amplitude is:
Magnitude = log10 (Amplitude) - 3
where the amplitude is measured in microns.
Assuming the amplitude of the earthquake is 100,000 microns, we can calculate its magnitude as:
Magnitude = log10 (100,000) - 3
Magnitude = 5 - 3
Magnitude = 2
Therefore, the magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale.
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Assume that the test scores of a college entrance test fits a normal distribution. The mean test score is 72, and the standard deviation is 15.2 a)What is the percentage of students scoring 84 or more? b) If a random student is chosen. What is the probability of the student scoring an 84 or more on the test if the max score was 95?
The probability of a random student scoring 84 or more if the maximum score is 95 is approximately 0.1179 or 11.79%.
To find the percentage of students scoring 84 or more, first we need to calculate the z-score using the formula:z = (X - μ) / σwhere X = 84, μ = 72, and σ = 15.2z = (84 - 72) / 15.2z = 0.7895Using a standard normal table or a calculator, we can find the percentage of students scoring 84 or more as:percentage = 1 - P(Z < 0.7895)percentage ≈ 21.4%Therefore, approximately 21.4% of students will score 84 or more on the test.b) To find the probability of a random student scoring 84 or more if the maximum score is 95, we need to first calculate the z-score using the same formula as before:z = (X - μ) / σwhere X = 84, μ = 72, and σ = 15.2z = (84 - 72) / 15.2z = 0.7895Then, we need to convert this z-score to a new z-score based on the maximum score of 95. Using the formula:z = (X - μ) / (max score - μ)σwhere X = 84, μ = 72, σ = 15.2, and max score = 95z = (84 - 72) / (95 - 72)z ≈ 1.19Using a standard normal table or a calculator, we can find the probability of a student scoring 84 or more as:P(Z > 1.19)P(Z > 1.19) ≈ 0.1179Therefore, the probability of a random student scoring 84 or more if the maximum score is 95 is approximately 0.1179 or 11.79%.
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WILL GIVE BRAINLIEST!!!
Question 1: The perimeter of the triangle below is 5x^3 - 2x^2 + 3x - 8.
Part A: Given the information below. What is the total length of sides 1 and 2 of the triangle? SHOW ALL WORK! (MANDATORY)
Side 1: 3x^2 - 4x - 1
Side 2: -x^2 + 4x + 5
Answer: Side 1 + Side 2 = _______ (MANDATORY)
Part B: What is the length of the 3rd side of the triangle? Show your work.
5x^3 - 2x^2 + 3x - 8 - (________) =
Answer (Drag & Drop):
A) 5x^3 - 4x^2 + 3x - 4
B) 5x^3 - 4x^2 + 3x - 12
C) 5x^3 - 4x^2 + 3x + 12
D) 5x^3 - 4x^2 + 3x + 4
Answer:
Part A:
To find the total length of sides 1 and 2 of the triangle, we need to add the lengths of these sides:
Side 1 + Side 2 = (3x^2 - 4x - 1) + (-x^2 + 4x + 5)
Simplifying the expression by combining like terms, we get:
Side 1 + Side 2 = 2x^2 + 1
Therefore, the total length of sides 1 and 2 of the triangle is 2x^2 + 1.
Part B:
To find the length of the 3rd side of the triangle, we can subtract the sum of sides 1 and 2 from the perimeter of the triangle:
5x^3 - 2x^2 + 3x - 8 - [(3x^2 - 4x - 1) + (-x^2 + 4x + 5)]
Simplifying the expression by distributing the negative sign, and then combining like terms, we get:
5x^3 - 2x^2 + 3x - 8 - 2x^2 + 8x + 4
Simplifying further by combining like terms, we get:
5x^3 - 4x^2 + 11x - 4
Therefore, the length of the 3rd side of the triangle is 5x^3 - 4x^2 + 11x - 4.
Answer:
A) 5x^3 - 4x^2 + 3x - 4
Step-by-step explanation:
Answer:
A) 5x^3 - 4x^2 + 3x - 4
Step-by-step explanation:
Part A:
To find the total length of sides 1 and 2 of the triangle, we need to add the lengths of these sides:
Side 1 + Side 2 = (3x^2 - 4x - 1) + (-x^2 + 4x + 5)
Simplifying the expression by combining like terms, we get:
Side 1 + Side 2 = 2x^2 + 1
Therefore, the total length of sides 1 and 2 of the triangle is 2x^2 + 1.
Part B:
To find the length of the 3rd side of the triangle, we can subtract the sum of sides 1 and 2 from the perimeter of the triangle:
5x^3 - 2x^2 + 3x - 8 - [(3x^2 - 4x - 1) + (-x^2 + 4x + 5)]
Simplifying the expression by distributing the negative sign, and then combining like terms, we get:
5x^3 - 2x^2 + 3x - 8 - 2x^2 + 8x + 4
Simplifying further by combining like terms, we get:
5x^3 - 4x^2 + 11x - 4
Therefore, the length of the 3rd side of the triangle is 5x^3 - 4x^2 + 11x - 4.
Answer:
A) 5x^3 - 4x^2 + 3x - 4
HELP! I WILL MAKE YOU BRAINLIEST
The intensity of sound from the stands of a football game is 30 times as great when the home team scores a touchdown as it is when the away team scores. Find the difference in the loudness of the sound when the two teams score. Round your answer to the nearest hundredth.
The difference in the loudness of sound is about _______ decibels
The difference in the loudness of sound when the two teams score is about 14.77 decibels
What is sound intensity ?Sound intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.
We can use the fact that the loudness of sound is measured in decibels (dB) and that the dB scale is logarithmic.
Let's assume that the loudness of the sound when the away team scores is x decibels. Then the loudness of the sound when the home team scores a touchdown is 30 times as great, which means it is 30x decibels.
The difference in loudness between the two scenarios is given by the difference in decibels:
difference in decibels = 10 log (30x/x) = 10 log 30 = 14.77
Therefore, the difference in the loudness of sound when the two teams score is about 14.77 decibels
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The diameter of a circle is 17 ft. Find its area to the nearest whole number.
Answer:
[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the area of a circle.}[/tex]
[tex]\textsf{First, we should identify the formula for the area of a circle.}[/tex]
[tex]\large\underline{\textsf{Formula:}}[/tex]
[tex]\mathtt{Area = \pi (radius)^{2}}[/tex]
[tex]\textsf{The radius is \underline{half} of the diameter.}[/tex]
[tex]\mathtt{\frac{17}{2} = 8.5ft.}[/tex]
[tex]\textsf{Let's begin solving for the area.}[/tex]
[tex]\large\underline{\textsf{Substitute:}}[/tex]
[tex]\mathtt{Area = \pi (8.5)^{2}}[/tex]
[tex]\mathtt{Area = 72.25 \pi}[/tex]
[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]
What is the perimeter of DEFG?
A 2-dimensional graph with an x-axis and a y-axis is given. A parallelogram DEFG is drawn on it with co-ordinates (2,1), (3,4), (7, 5) and (6,2) respectively.
The perimeter of DEFG will be 2(√10+√17).
What are spherical cοοrdinates?The cοοrdinate system that is mοst frequently emplοyed in three-dimensiοnal systems is called spherical cοοrdinates οf the system, represented as (r,Ф,∅ ).
The surface area in three dimensiοns is calculated using the spherical cοοrdinate system. Radial distance, pοlar angles, and azimuthal angle are the three numbers that these cοοrdinates indicate. Additiοnally knοwn as spherical pοlar cοοrdinates.
A 2-dimensiοnal graph with an x-axis and a y-axis is given.
A parallelοgram DEFG is drawn οn it with cο-οrdinates (2,1), (3,4), (7, 5) and (6,2) respectively.
Sο the perimeter will be DE = √10
DG=√17
EF = √17
FG=√10
Sο the perimeter will be 2(√10+√17).
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. Evaluate: 2(6+4) – 3(5) 1 70 85 5
Answer:
5
Step-by-step explanation:
2(6+4) – 3(5)
= 12 + 8 - 15
= 20 - 15
= 5
So, the answer is 5
Cocoa Puffs family size was once 19.3 oz, now it is 18.1 oz. By what percent did the product
"shrink"? Show your work.
so it shrunk by 19.3 - 18.1 = 1.2.
so if we take 19.3(origin amount) as the 100%, what's 1.2 off of it in percentage.
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 19.3 & 100\\ 1.2& x \end{array} \implies \cfrac{19.3}{1.2}~~=~~\cfrac{100}{x} \\\\\\ 19.3x=120\implies x=\cfrac{120}{19.3}\implies x\approx 6.22[/tex]
Mr. Sharma has the option of selecting a rectangular plot of size 45 m × 25 m or a square plot of
size 35 m at the same price. Which one should he prefer and why?
Answer:
Square Plot
Step-by-step explanation:
Let us compare the Area of both plots
Rectangular Plot : L X B = 45 x 25 = 1125 M^2
Square Plot : S X S = 35 x 35 = 1225 M^2
Area of Square Plot > Area of Rectangular Plot
Therefore he should prefer the Square Plot as it has more area.
Hope it helps.
How long is the base of a parallelogram if it has an area of 60 square feet and a height of 10 feet? 6 feet 50 feet 60 feet
Answer:6 feet
Step-by-step explanation:
The formula for the area of a parallelogram is:
Area = base x height
We know that the area is 60 square feet and the height is 10 feet, so we can plug these values into the formula and solve for the base:
60 square feet = base x 10 feet
Dividing both sides by 10 feet gives:
6 feet = base
A cylindrical soup can is 6 cm in diameter and 12 cm tall.
A. If the diameter is 6 cm, what is the radius?
B. We use the formula to find the surface area of a cylinder (with r = radius & h = height).
C. Plug your "r", "h", and " 3.14 for n" into the formula.
Show your work and label your final answer to find the surface area of the soup can.
Please only help me if your going to help
Answer:
A. If the diameter is 6 cm, then the radius is half of that:
radius = 6 cm / 2 = 3 cm
B. The formula for the surface area of a cylinder is:
S.A. = 2πr^2 + 2πrh
C. Plugging in the values for r, h, and π:
S.A. = 2π(3 cm)^2 + 2π(3 cm)(12 cm)
S.A. = 2π(9 cm^2) + 2π(36 cm^2)
S.A. = 18π cm^2 + 72π cm^2
S.A. = 90π cm^2
Therefore, the surface area of the soup can is 90π square centimeters. This can be simplified to approximately 282.74 square centimeters by using the value 3.14 for π.
HELP PLEASE ASAP!!!!
Triangle PQR with coordinates P(-3,4). Q(-6,1), and R(-6,6) is reflected over the x-axis. List the coordinates of the new image
Answer:
P(0,2), Q(3,5), R(3,0)
Step-by-step explanation:
The radius of circle B
is 4 centimeters and the circumference of
Circle A is 30 pi
centimeters. Find CD.
Find CD:
Let,
[tex]r_1[/tex] be a radius of Circle A
[tex]r_2[/tex] be a radius of Circle B
Given:
[tex]r=4cm.[/tex]
Circumference: [tex]2\pi r[/tex]
[tex]2\pi r_1=30[/tex]
[tex]r_1=\dfrac{15}{\pi }[/tex]
[tex]CD=D_1+D_2[/tex]
[tex]=2r_1+2rx_2[/tex]
[tex]=2\times(\dfrac{15}{\pi })+2\times4[/tex]
[tex]CD=17.55cm.[/tex]
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Mr Keag's swimming pool is 15 feet long, 12 feet wide and 10 feet deep. How much water would it take to fill it half way to the top
Answer:
900 cubic feet
Step-by-step explanation:
[tex] \frac{1}{2} (15 \times 12 \times 10) = \frac{1}{2} (1800) = 900[/tex]
what is value expression
1.3(X + 2)-(y - 6)
when X= 4 and Y= 2
a 1.1
b 11.8
c 2.6
d 26
The value of the expression 1.3(x + 2) - (y - 6) when x = 4 and y = 2 is Option B: 11.8.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
To find the value of the expression 1.3(x + 2) - (y - 6) when x = 4 and y = 2, we substitute these values into the expression and simplify -
Substitute the values x = 4 and y = 2 into the expression -
1.3(x + 2) - (y - 6)
= 1.3(4 + 2) - (2 - 6)
Apply the addition and subtraction operation -
= 1.3(6) - (-4)
Apply the multiplication operation -
= 7.8 + 4
= 11.8
Therefore, the value of the expression is 11.8.
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A grocer has two kinds of candy, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
Answer:The quantity of grocer of price $1.40 is 45 pounds
The quantity of grocer of price 40 cents is 55 pounds
Step-by-step explanation:
Let The quantity of one grocer = x pound
Let The quantity of other grocer = y pound
The selling price of x grocer = 40 cents per pound
The selling price of y grocer = $ 1.40 per pound = 1.40 × 100 = 140 cents
Total quantity = 100 pounds
Total price of both grocer = 85 cents
According to question
x + y = 100 .........A
And
40 × x + 140 y = 85 × 100
Or, 40 x + 140 y = 8500 ........B
Solving eq A and eq b
(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100
Or, (40 x - 40 x) + (140 y - 40 y) = 8500 - 4000
or, 0 + 100 y = 4500
∴ y =
i.e y = 45 pounds
So, The quantity of grocer of price $1.40 = y = 45 pounds
Again
Put the vaue of y in eq A
x + y = 100
i.e x = 100 - y
or, x = 100 - 45
∴ x = 55 pounds
So, The quantity of grocer of price 40 cents = x = 55 pounds
Hence, The quantity of grocer of price $1.40 is 45 pounds
And The quantity of grocer of price 40 cents is 55 pounds Answer
A screen door spring has a spring constant of 188 N/m, and stretches 0. 292 m when the door is opened. What force does it exert?
(Unit = N)
If the screen door spring has a spring constant of 188 N/m, then the force it exert is 54.9 N .
The force exerted by the screen door spring can be calculated using Hooke's law,
The Hooke's Law states that the force exerted by a spring is directly proportional to its spring constant and the amount it is stretched.
The formula for "Hooke's-law" is ⇒ F = kx
Where F is = force exerted by spring, k is = spring constant, and x is = amount spring is stretched.
In this case , the spring constant(k) = 188 , the distance stretched(x) = 292m ;
Substituting the values,
We get,
⇒ F = (188 N/m)(0.292 m)
⇒ F = 54.896 N
⇒ F ≈ 54.9N
Therefore, The force exerted by the screen door spring is approximately 54.9 N.
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