31. PHOTOGRAPHY The length and width of a 6-inch by 8-inch
the same amount to make a new photograph whose area is half that of the original. By
how many inches will the dimensions of the photograph have to be reduced?
Answers
Answer:
The dimension has to be reduced by two inches.
Step-by-step explanation:
Given that the dimensions are: 6 by 8 inches which means that the area is 48 square inches.
Let x be the amount to make a new photo which is half of the area that means
The new dimensions will be: (8-x) by (6-x) and as the area is half
The area of new photo will be: 48/2 = 24
Putting it mathematically (Look at the solution above).
Subtracting 12 from both dimensions will make them negative so 12 cannot be the solution.
Hence, the dimensions have to be reduced by 2 inches
Related Questions
somebody help me find m∠DEC.
Answers
Answer:
should be 96 degrees
Step-by-step explanation:
Answer:100
Step-by-step explanation:
Find the equation of the line use exact numbers.
Y=|____|x+|____|
Answers
Answer:
\(y=\frac{3}{4} x-2\)
Step-by-step explanation:
The line has a positive slope, that much is clear. If we just count from the y-intercept up to the next clear point, we can see that it is 3 up and 4 to the right. That gives us a rise over run of 3 over 4, or \(\frac{3}{4}\).
The y-intercept is -2, so that is the latter half of the equation.
ILL GIVE BRAINLY
Slope = 1/2
y-intercept = 7
Answers
Answer:
b
Step-by-step explanation
since its y=mx+y the y intercept is 7 and the slope is 1/2 you plug them in the formula and get 1/2x+7 since mx is the slope and y is the y intercept
d might look the right answer but its not since its 1/2y+7
a and c are wrong because the slope an y intercepts are flipped it should be the other way around
ANSWER:
B
Can u guys please answer this question. This is extremely urgent
The cross-sections of the solids are sectors. Find the surface area, rounding your answer to 1 decimal place.
Answers
Answer:
The total surface area of the figure is approximately 10.2 m²
Step-by-step explanation:
The dimensions of the solid are;
The shape of the solid = An half cylinder
The diameter of the cylinder, D = 1.6 m
The length of the cylinder, l = 2 m
The surface area of the curved part of the solid = π × D × l ÷ 2
Therefore;
The surface area of the curved part of the solid = π × (1.6 m) × 2 m/2 ≈ 5.03 m²
The area of the curved surface, V = 5.03 m²
The area of the rectangular top, A = 1.6 m × 2 m = 3.2 m²
The area surface of the semi-circular sides of the figure = 2 × π·D²/4 ÷ 2
Therefore;
The area surface of the semi-circular sides of the figure = 2 ×π × (1.6 m)²/4 ÷ 2 ≈ 2.01 m²
The total surface area of the figure, A = 5.03 m² + 3.2 m² + 2.01 m² = 10.24 m²
The total surface area of the figure ≈ 10.2 m² (rounding to 1 decimal place)
Courtney remembers that her ATV has 6gallons of gas in the tank on Monday. She is using gas at a rate of 3gallons for 45miles.A). Write a linear equation that represents the number of "Y" gallons left in the tank after "X" miles.B). Graph the linear equationC). How many gallons will be left after 90miles
Answers
EXPLANATION:
The reason or proportion that arises in the exercise is:
\(\begin{gathered} \frac{y}{x}=\frac{3}{45} \\ \frac{3}{45}=0.066 \\ \text{the constant or porpor}tion\text{ is :0.066} \end{gathered}\)A.Now knowing the constant or proportion we can formulate an equation:
(ANSWER A:)
\(\begin{gathered} y=(x)(0.066) \\ \text{where x is }time\text{ in miles }for\text{ the constant} \end{gathered}\)Multiplying any time in miles by the constant will give us the number of gallons consumed in y.
B.Now to graph the linear equation we must give x values to obtain the values for gallons of gas.(ANSWER B)
To have the values in x we can use the ones shown in the graph:
\(\begin{gathered} -y=(x)(0.066) \\ y=(5)(0.066) \\ y=0.33 \\ -y=(x)(0.066) \\ y=(10)(0.066) \\ y=0.66 \\ -y=(15)(0.066) \\ y=0.99 \\ -y=(20)(0.066) \\ y=1.32 \\ -y=(25)(0.066) \\ y=1.65 \end{gathered}\)With the previous data we can graph.:
the graph is as follows:
In the graph we can see that as time progresses the gallons of gasoline consumed increases constantly.
C.To find out how many gallons of gasoline are left after 90 miles we must use the equation we found and replace the value of 90 miles in x, so we will know if after that time there is still gasoline.(ANSWER C)
\(\begin{gathered} y=(x)(0.066) \\ y=(90\text{ miles})(0.066) \\ y=6\text{ } \\ \text{The answer is }\colon After\text{ 90 miles }all\text{ 6 gallons of gasoline }have\text{ } \\ \text{been used.} \end{gathered}\)
20 Points Please Help
Answers
That’s all I know from this I apologize, I’m only a freshman in hs lol
Good luck and Merry Christmas, happy holidays
If a study shows a result with a P value of 0.2, what does that mean? A)There is an 80 percent chance the relationship being studied is real. B)There is a 0.8 percent chance the relationship being studied is real. C)There is a 0.2 percent chance the relationship being studied is real. D)There is a 20 percent chance the relationship being studied is real.
Answers
There is a 20 percent chance the relationship being studied is real. Option D
If a study shows a result with a P value of 0.2, it means that there is a 20 percent chance that the observed relationship being studied is due to random chance or sampling variability.
In other words, the P value represents the probability of obtaining a result as extreme as, or more extreme than, the observed result if the null hypothesis were true.
The null hypothesis assumes that there is no real relationship or effect in the population being studied. The alternative hypothesis, on the other hand, suggests that there is a real relationship or effect. The P value helps determine the strength of evidence against the null hypothesis.
A P value of 0.2 means that if the null hypothesis were true (i.e., there is no real relationship), there would be a 20 percent chance of obtaining a result as extreme as, or more extreme than, the observed result by random chance alone.
This implies that the observed result is not statistically significant at conventional levels of significance (typically set at 0.05 or 0.01), which means there is not enough evidence to reject the null hypothesis.
Therefore, the correct answer is (D) There is a 20 percent chance the relationship being studied is real. It's important to note that the P value does not directly indicate the probability of the relationship being true or real, but rather the probability of obtaining the observed result under the assumption of no relationship. Option D
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Transform the following vectors into cylindrical and spherical coordinates: i. D=(x+z )ay ii. E=(y2 −x 2 )ax
+xyzax +(x2 −z2 )az
Answers
The vector D in cylindrical coordinates is given as D = (r + z) a_θ, and in spherical coordinates, it is D = (r + z) sin(θ) a_ϕ. The vector E in cylindrical coordinates is E = (r^2 - x^2) a_r + (rxy) a_θ + (x^2 - z^2) a_z, and in spherical coordinates, it is E = (r^2 - x^2) a_r + (rxy) sin(θ) a_ϕ + (x^2 - z^2) cos(θ) a_θ.
For vector D, we can express it in cylindrical coordinates by noting that r = √(x^2 + y^2) and θ = arctan(y/x). Therefore, D = (x + z) a_y can be rewritten as D = (r + z) a_θ, where a_θ is the unit vector in the θ direction.
To convert D into spherical coordinates, we use the relationships r = √(x^2 + y^2 + z^2), θ = arctan(y/x), and ϕ = arccos(z/r). So, D = (x + z) a_y becomes D = (r + z) sin(θ) a_ϕ, where a_ϕ is the unit vector in the ϕ direction.
For vector E, in cylindrical coordinates, we can express it as E = (r^2 - x^2) a_r + (rxy) a_θ + (x^2 - z^2) a_z. Here, a_r, a_θ, and a_z are the unit vectors in the radial, azimuthal, and axial directions, respectively.
To convert E into spherical coordinates, we still use the same relationships for r, θ, and ϕ. Therefore, E = (r^2 - x^2) a_r + (rxy) a_θ + (x^2 - z^2) a_z can be transformed into E = (r^2 - x^2) a_r + (rxy) sin(θ) a_ϕ + (x^2 - z^2) cos(θ) a_θ.
By applying the appropriate coordinate transformations, we can express the given vectors D and E in both cylindrical and spherical coordinates.
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Solve |y-2|<10
please
Answers
Y=(-8, 12)
Wouldnt the answer be anything above 12? Because if Y is unknown, and you're taking 2 away from it, and it still has to be greater than 10, then it should be anything above 12. Unless it's saying that the number is greater than 10, and you are just taking away 2 from a number and it doesn't have to be greater than 10.
How does the shape of a t-distribution with a small df compare with a normal distribution?
Answers
When compared to a normal distribution, a t-distribution with a small degrees of freedom has heavier tails, indicating a higher probability of extreme values. As the degrees of freedom increase, the shape of the t-distribution approaches that of a normal distribution.
The shape of a t-distribution with a small degrees of freedom (df) differs from that of a normal distribution. The first paragraph provides a summary of the answer, and the second paragraph explains the details of the comparison.
A t-distribution with a small degrees of freedom has a shape that is similar to a normal distribution, but with heavier tails. As the degrees of freedom decrease, the t-distribution becomes more spread out and has a higher probability of extreme values compared to a normal distribution.
The tails of the t-distribution are fatter or thicker than those of a normal distribution. This means that the t-distribution has a higher probability of extreme values, making it more likely to observe values far away from the mean. In contrast, the normal distribution has thinner tails, indicating a lower probability of extreme values and a higher concentration of data around the mean.
The shape of the t-distribution approaches that of a normal distribution as the degrees of freedom increase. When the degrees of freedom are large (typically above 30), the t-distribution becomes very similar to a normal distribution, and the differences between them become negligible.
The t-distribution is widely used in statistical inference, especially in situations where the sample size is small or when the population standard deviation is unknown. It provides a more appropriate distribution for estimating population parameters when the underlying data exhibit variability.
In summary, compared to a normal distribution, a t-distribution with a small degrees of freedom has heavier tails, indicating a higher probability of extreme values. As the degrees of freedom increase, the shape of the t-distribution approaches that of a normal distribution.
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factor the expression using the GCF 6x+24
Answers
Answer:
6(x+4)
Step-by-step explanation:
The GCF is 6 thus factor the expression
The given expression 6x + 24 can be factored using the GCF as 6(x + 4).
What is the Factorization?Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original. For example, the number 21 factors into primes as 3 × 7, and the polynomial x² − 9 factors as (x+3)(x-3).
The expression is given in the question as:
6x + 24
The expression 6x + 24 can be factored using the greatest common factor (GCF) as follows:
⇒ 6x + 24 = (6x + 24) / 6 × 6
The GCF of 6x + 24 is 6, so we can divide both terms by 6 to get:
⇒ 6x + 24 = (x + 4) × 6
We can then factor out the common factor of 6 to get:
⇒ 6x + 24 = 6(x + 4)
Thus, the given expression 6x + 24 can be factored using the GCF as 6(x + 4).
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Lily wants to buy a cow but can't afford the $25 it costs. Later in the year it is at an affordable $15 and Lily can buy it. What percentage of a
discount was on the cow? Please explain :)
Answers
Answer:
There was 60% discount on the cow.
Step-by-step explanation:
Cost of cow = $25Latest price = $15Discount can be calculated by dividing the latest price by the original price and multiplying by 100.
Thus,
percentage discount = 15/25 × 100
= 0.6 × 100
= 60%
Thus, there was 60% discount on the cow.
In the following exercises, multiply the binomials. Use any method.
248. (m + 11)(m − 4)
Answers
Answer:
Hence the expression \($$(m+11)(m-4)=m^2+7m-44$$\)
Step-by-step explanation:
Explanation
The given expression is (m+11)(m-4).We have to multiply the given expression.Multiply the (m+11) by -4, multiply the (m+11) by m then add like terms.\($$\frac{\begin{matrix}{} & {} & m & + & 11 \\ \times & {} & m & - & 4 \\ \end{matrix}}\)
_____________
\({\frac{\begin{matrix}{} & - & 4m & - & 44 \\ {{m}^2} & + & 11m & {} & {} \\ \end{matrix}}{\begin{matrix}{{m}^2} & + & 7m & - & 44 \\ \end{matrix}}}$$\)
Helppp pleasee ........
Answers
to solve this you just substitute 4 in for x into the equation and solve for y. since negative 3 plus 7 is 4, y=4
Answer:
y=3
Step-by-step explanation:
y = - x +7
x=4
so y = -4 +7
y = 3
Please help me Brainliest for the first to answer or for whoever is correct... Please please please help me
As a construction manager, you are asked to build a new road, which crosses the point (1,0). There is another road already built, which can be expressed as y = -1/2 X − 3. You are asked to build your road such that it crosses this road at a perpendicular angle. Find the correct value for a and b in the following equation of your road. y = + b
Write your answer as an equation in slope-intercept form.
Thank you!
Answers
Answer:
y=2x+b
0=2×1+b
-2=b
y=2x-2
The following table gives the number of people infected by the flu over a given number of months.
Number of Months
0
1
2
3
4
5
Number of People Infected
1
5
13
33
78
180
Describe any trends or patterns that you observe.
a.
The number of people infected is decreasing at a steady rate.
b.
The number of months is increasing quickly.
c.
The number of people infected is increasing at a very fast rate.
d.
There is no apparent trend or pattern in the table.
Answers
The correct option is C. The number of people infected is increasing at a very fast rate.
The given table relates the data of the number of months corresponding to which the number of people infected by the flu.
According to the table, as the number of months is increasing by 1 simultaneously the number of people affected by the flu is rising at more than double the rate.
Therefore, the correct option is C as the trend of the given table is best described by option C. People are affected more and more by the flu in a 1-month duration only.
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A circular dartboard has diameter 40cm. Its bull’s eye has diameter of 8 cm. if an amateur throws a dart and it hits the board, what is the probability that the dart hits the bull’s eye.
Answers
Answer:
a value of is required in the following exercises, use
A circular dartboard has diameter 40 Its bull's eye has diameter 8
a. If an amateur throws a dart and it hits the board. What is the probability that the dart hits the bull's eye?
b. After many throws, 75 darts have hit the target. Estimate the number hitting the bull's eye.
Step-by-step explanation:
hope it helps! please mark brainlets
5. Oshaunda buys a car that costs $21,000. It depreciates at 8.2% per year. a. Write an equation for the value of the car. V=21,000(1-0.082) V-21,000(0.918) B. Oshaunda tries to sell the car 4 years later. What is the car worth when it is 4 years old? Hint: Use your formula for part (a), and plug in t = 4. Use GEMA to finish the math.
Answers
Answer:
a.
\(f(t) = 21000( {.918}^{t} )\)
b.
\(f(4) = 21000( {.918}^{4}) = 14913.86\)
184 sixth graders are going on a field trip. There needs to be one chaperone for every four students. If a bus can hold 50 people, how many busses will they need for the trip? Hint: You can't use part of a bus! *
Answers
Answer:
5 buses
Step-by-step explanation:
Total number of 6th graders going for the field trip = 184
Step 1
Divide the total number of students by 4
184/4 = 46
We have 46 groups of six graders.
Step 2
There needs to be one chaperone for every four students.
We have 46 groups of six graders
This means there is need for 1 chaperone per group
Hence, we have 46 chaperones
Step 3
Find total number of people going for the field trip
184 students + 46 chaperones
= 230 people
Step 4
If a bus can hold 50 people, how many buses will they need for the trip?
50 people = 1 bus
230 people = ??y
50 × y = 230
y = 230/50
y = 4.6 buses
Hence, 4.6 buses would be needed but since we can't have 0.6(part) of a bus figuratively, as buses come in whole numbers, we approximate to the nearest whole number
= 4.6 ≈ 5
Therefore, they would be needing 5 buses for the trip.
5 buses
Step-by-step explanation:
i got 10 out of 10
Shawn bought a 10-pound turkey to serve for Thanksgiving. He plans to serve eachadult 2/5 of a pound.Write an equation to represent the number of adult servings, x, Shawn canget from the 10-pound turkey. Use your equation to determine the number of adultservings.
Answers
Since each serving contains 2/5 of a pound, then, the total weight of x servings would be:
\(\frac{2}{5}x\)If the total weight of x servings should be equal to the weight of the turkey, then:
\(\frac{2}{5}x=10\)Multiply both sides of the equation by 5/2:
\(\frac{5}{2}\cdot\frac{2}{5}x=\frac{5}{2}\cdot10\)Simplify the expressions on both sides of the equation:
\(x=25\)Therefore, the number of adult servings from a 10 pound turkey, will be 25.
For the linear regression y = ẞ1 + ẞ2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 +681 +382 + 18ẞ1ẞ2
Derive the partial derivatives of SSE with respect to B1 and B2 and solve the optimal values of these parameters.
a. B₁ = B1
b. B₂ =
Answers
The optimal values of these parameters are:
a. β₁ = 0
b. β₂ = 0
The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 + 681 + 382 + 18β1β2
Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.
Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0
Now, we need to find the partial derivative of SSE with respect to β1.
∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0
Therefore, we obtain the optimal value of β2 as 0.
Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0
Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.
Thus, the optimal values of β1 and β2 are 0 and 0, respectively.
Therefore, the answers are: a. β₁ = 0 b. β₂ = 0
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I need assistance with this problem 2 ^ 6 * 8 ^ 6
Answers
Forrest Lumber purchased a table saw for $960. After 3 years the saw had a depreciated value of $600. What is the amount of yearly depreciation?
Answers
Answer:
subtract to get the depreciation;
$960-$600=$360
therefore;if 3years =$360
1year=??
cross multiply:1×360 divided by 3
=$120
A car is driving at 88 kilometres an hour I’m Europe how fast is the car going in miles per hour. One kilometer = 0.62 mile.
Answers
Set up an equation.
88km/1hour x 0.62mile/1km
88 x .62 = 54.56
The car is going 54.56 mph.
Hope this helps
Use substitution: y= 5 and y = 7x -2*
Answers
Answer:
x = 1
Step-by-step explanation:
y = 5 y = 7x - 2
5 = 7x -2
-7x -7x
-7x + 5 = -2
-5 -5
-7x = -7
x = 1
Eric starts picking strawberries after Jody had already picked 12 pounds. If Eric picks at a rate of 8 pounds
per hour and Jody picks at a rate of 6 pounds per hour, how many whole hours after Eric starts picking will
the total weight of picked strawberries exceed 100 pounds? Explain how you found your answer.
Answers
Answer:
It will take him eight hours to get to one hundred pounds of strawberries/ nine hours to get to one hundred and eight pounds
Step-by-step explanation
H - hours 8 represents number of lbs Eric picks in H amount of hours
8h + 12 = 100
-12 -12
8h= 88
8h/8= 88/8
H=8
. Excel Secondary School wants to send its students for an educational trip and has found an organisation that is willing to sponsor up to an amount of $2 500 for the trip. Given that the cost of sending a student for the trip is $12, what is the maximum number of students the school can send for the trip if it relies only on the sponsorship?
Answers
Answer:
208 students I think that's the answer
A triangle has a perimeter of 7x 8. the first side of the triangle has a length of 3x, and the second side has a length of 2x − 5. what is the length of the third side of the triangle? x 13 2x 13 5x − 5 12x 3
Answers
The length of the third side of the triangle with a perimeter of 7x + 8 is 2x + 3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
A triangle is a polygon that has three sides. The perimeter of a triangle is the sum of all the three sides.
Hence:
Perimeter of triangle = side 1 + side 2 + side 3
A triangle has a perimeter of 7x + 8. the first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.
Hence:
Perimeter of triangle = side 1 + side 2 + side 3
7x + 8 = 3x + (2x - 5) + side 3
7x + 8 = (5x - 5) + side 3
side 3 = 7x + 8 - (5x - 5)
side 3 = 2x + 13
The length of the third side is 2x + 3
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teacher: how can we change the base of a logarithm? student:
Answers
We can change the base formula by:
logₐ b = logₓ a /logₓ b
OR
logₓ a, logₓ b = logₓ a
The change of base formula is used to change the base of a logarithm. We know that "log" stands for a logarithm of base 10 and "ln" stands for a logarithm of base e. But there is no option to calculate the logarithm of a number with any other bases other than 10 and e.
The change of base formula solves this issue of changing base from e to 10, and from base 10 to e. Also, it is used in solving several logarithms problems.
Base Formula: -
The change of base formula is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm. This is a property of logarithms. You can see the change of base formula here.
Change of base formula
logₐ b = logₓ a /logₓ b
OR
logₓ a, logₓ b = logₓ a
Change of Base Formula
Change of base formula can be represented as follows. Here the base of the given logarithm is also changed to a logarithm with a new base. The basic logarithm with a base is transformed to two logarithms with a new and same base. The change of base formula is:
logₐ b = [logₐ x] / [logₐ y]
In this formula,
The argument of the logarithm in the numerator is the same as the argument of the original logarithm.The argument of the logarithm in the denominator is the same as the base of the original logarithm.The bases of both logarithms of numerator and denominator should be the same and this base can be any positive number other than 1.Change of Base Formula Derivation
Change of base formula derivation can be understood from the following steps. Let us assume that
log ₐ b = p, logₙ a = q, and logₙ b = r.
By converting each of these into exponential form, we get,
a = \(b^{p}\), a = \(x^{q}\), and b = \(n^{r}\)
From the first two equations,
\(x^{q}\) = \(n^{r}\)
Substituting b = \(n^{r}\) (which is from third equation) here,
(\(n^{r}\))\(^{p}\) = \(x^{q}\)
\(n^{r}\))\(^{p}\) = \(x^{q}\)(Using a property of exponents)
p r = q
p = q / r
Substituting the values, we get,
logₐ b = [logₐ x] / [logₐ y]
For Example:
Evaluate the value of log₆₄ 8 using the change of base formula.
Solution:
We will apply the change of base formula (by changing the base to 10). Note that log₁₀ is same as log.
log₆₄ 8 = [log 8] / [log 64]
= [log 8] / [log 82]
= [log 8] / [2 log 8] [∵ log am = m log a]
= 1 / 2
Answer: log₆₄ 8 = 1 / 2
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4 letters are typed, with repetition allowed. what is the probability that all 4 will be vowels? write your answer as a percent. round to the nearest hundredth of a percent as needed.
Answers
Answer:
There are 5 vowels in the English alphabet: A, E, I, O, and U. Since repetition is allowed, each letter can be any one of the 5 vowels.
The probability of the first letter being a vowel is 5/26, since there are 5 vowels out of 26 letters in total. The probability of the second letter being a vowel is also 5/26, and so on for the third and fourth letters.
Since the events of each letter being a vowel are independent, we can use the multiplication rule to find the probability of all four letters being vowels:
P(all 4 vowels) = (5/26) x (5/26) x (5/26) x (5/26) = (5/26)^4
Using a calculator, we get:
P(all 4 vowels) ≈ 0.0023
To express the answer as a percent, we multiply by 100:
P(all 4 vowels) ≈ 0.23%
Therefore, the probability that all 4 letters typed will be vowels, with repetition allowed, is approximately 0.23%.
Step-by-step explanation: