Answer: The simplest form of 564/18 is 94/3.
Step-by-step explanation: Hope this helps
The question is In the image
the probability of the marble landing on either a 00 or black slot is 19/38 or approximately 0.5.
how to solve probability?
There are 38 possible outcomes for a single spin of the American roulette wheel. Out of these 38 slots, two are labeled 0 and 00, and half of the remaining 36 slots are red and half are black.
Therefore, the probability of the marble landing on a black slot is 18/38 or 9/19. This is because there are 18 black slots out of a total of 38 slots.
Similarly, the probability of the marble landing on a 00 slot is 1/38.
To find the probability of the marble landing on either a 00 or black slot, we can add the probabilities of these two events. That is,
P(00 or black) = P(00) + P(black)
= 1/38 + 9/19
= (1 + 18)/38
= 19/38
Therefore, the probability of the marble landing on either a 00 or black slot is 19/38 or approximately 0.5.
It is important to note that while the probability of winning on a single bet in roulette may seem attractive, the game has a high house edge, meaning that the odds are in favor of the casino. Therefore, it is important to gamble responsibly and within one's means.
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To make color RW689, Raul must mix 3 parts red pint with 11 parts white paint. What is the ratio of white paint color RW689?
The ratio of white paint to color RW689, given that Raul must mix 3 parts red paint with 11 parts white paint to form RW689, is 11:14 or 11/14.
What is the ratio?The ratio shows the relative size of one value or quantity when compared to another quantity.
Ratios are fractional or proportional values, which can be depicted as decimals, fractions, or percentages.
The mixture of red paint to white paint:
Red parts = 3
White parts = 11
Ratio of red to white = 3:11
The sum of ratios = 14 (3 + 11)
Therefore, color RW689 = 14 parts of red and white.
Thus, the ratio of white paint to color RW689 = 11:14 or 11/14
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Compare and contrast the effects that a proportional dimension change has on perimeter and area of figures.
like a sentence or a few
a proportional dimension change has a proportional effect on the perimeter, but a quadratic effect on the area of figures.
Define area of fig?
The area of a figure refers to the measurement of the region enclosed by the boundary of a two-dimensional shape or a flat surface. Square units like square inches, square feet, square metres, etc. are used to measure it.
A proportional dimension change in a figure occurs when all the sides are multiplied by the same factor. When this happens, the perimeter of the figure also changes proportionally to the factor of the dimension change. For example, if all the sides of a rectangle are multiplied by 2, the perimeter will also be doubled.
However, the area of the figure changes proportionally to the square of the factor of the dimension change. For example, if all the sides of a rectangle are multiplied by 2, the area will be multiplied by 4 (2²).
In summary, a proportional dimension change has a proportional effect on the perimeter, but a quadratic effect on the area of figures.
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Compare and contrast the effects that a proportional dimension change has on perimeter and area of figures?
please answer all of the following
1. Calculate the term (time of a simple interest loan that has earned $37.80 in interest on a principal of $450.00 and an interest rate of 1.4%/year.
Hint: i= Prt
P = S
r=
i= S
Find____
2. Calculate the interest rate of a simple interest loan where a principal amount of $425.00
has earned $286.88 in interest over 3 years.
Hint: I= Prt
P= $
t =
i = $
Find ____
3. Calculate the principal of a simple interest investment that earned $25.81 in interest for 8 months at an interest rate of 3.2%.
Hint: Remember 1 year = 12 months.
Time must be converted to years to be used in the formula.
8 months = 8/12 years
Hint: i = Prt
r=
t=
i=$
Find______
Consequently, the loan's duration is roughly 0.6 years the loan's interest rate is roughly 22.5%And the investment's principal is roughly $6,387.
Define investement and interest?An asset or thing is considered an investment if it is bought with the expectation that it may one day produce income or increase in value. A purchase of commodities that are not used right now but will be utilised to generate wealth down the road is referred to as an investment in the economic sense. Stocks, bonds, properties, and mutual funds are a few types of investments.
On the other hand, interest is the fee associated with the right to borrow money. Usually, it is stated as an annual percentage rate. (APR). The percentage of ownership a stockholder has in a firm is another definition of interest.
1. Using the formula below, we can determine the term (period) of a simple interest loan with a $450 principal, a 1.4% annual interest rate, and interest earnings of $37.80.
I = Prt
where I stands for interest earned, P stands for the principal, r represents the yearly interest rate in decimal form, and t stands for the amount of time in years.
Inputting the values provided yields:
37.80 = 450 * 0.014 * t
Simplifying this equation, we get:
t = 37.80 / (450 * 0.014)
(t 0.6 years)
2. Using the formula below, we can determine the interest rate for a simple interest loan with a $425.00 principal amount and $286.88 in interest accrued over three years:
I = Prt
where I stands for interest earned, P stands for the principal, r represents the yearly interest rate in decimal form, and t stands for the amount of time in years.
Inputting the values provided yields:
286.88 = 425 * r * 3
When we simplify this equation, we obtain:
r = 286.88 / (425 * 3)
r ≈ 0.225 or 22.5%
3. Using the technique below, we can determine the principal of an investment with simple interest that generated $25.81 in interest over the course of 8 months at an interest rate of 3.2%:
I = Prt
where I stands for interest earned, P stands for the principal, r represents the yearly interest rate in decimal form, and t stands for the amount of time in years.
First, we must convert the seconds to years:
8 months equals 8/12 years.
Inputting the values provided yields:
25.81 = P * 0.032 * (8/12)
When we simplify this equation, we obtain:
P = 25.81 / (0.032 * (8/12))
P ≈ $6,387
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A watch manufacturer believes that 60% of men over age 50 wear watches. So, the manufacturer took a simple random sample of 275 men over age 50 and 170 of those men wore watches. Test the watch manufacturer's claim at α = .05. (a) State the null and alternative hypothesis in symbolic form. (b) Find the test statistic (preferably obtained using technology). Sketch a graph of the normal distribution clearly showing the test statistic (rounded to two decimal places) and the critical region, α=.05. (c) Decide and explain your choice to reject the null or fail to reject the null. (d) Write a summary statement addressing the original claim
Answer:
A watch manufacturer believes that 60% of men over the age of 50 wear watches. So, the manufacturer took a simple random sample of 275 men over the age of 50, and 170 of those men wore watches. Test the watch manufacturer's claim at α = 0.5 using PHANTOMS.
Find the value of x:
With regards to the above geometry problems the value of x are given below.
a) Here x = 15
b) here x = 28
These are solved using proportions.
How does proportion help to solve the above problems?Proportion helps to solve the above problems by setting two ratios equal to each other and cross-multiplying to solve for the unknown variable, which satisfies the ratio relationship between the two quantities.
a)
To solve for x, we can cross-multiply the fractions and simplify:
x/20 = 9/12
Cross-multiply:
12x = 9 * 20
Simplify:
12x = 180
x = 15
Therefore, the solution to the equation x/20 = 9/12 is x = 15.
b)
To solve for x, we can cross-multiply the fractions and simplify:
15/(x-3) = 18/(x+2)
Cross-multiply:
15(x+2) = 18(x-3)
Simplify:
15x + 30 = 18x - 54
Subtract 15x from both sides:
30 = 3x - 54
Add 54 to both sides:
84 = 3x
Divide both sides by 3:
x = 28
Therefore, the solution to the equation 15/(x-3) = 18/(x+2) is
x = 28.
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Geometry task!!!
Please help for all three , a) , b) , and c)
The power emitted by the star's surface is much greater than the power generated by its interior.
How to explain the informationa) The power generated by the star's interior can be calculated using the formula for the volume of a sphere:
V = (4/3)πr³
V = (4/3)π(7x10^8)³ ≈ 1.41x10^27 cm³
Multiplying this volume by the power generated per cubic centimeter, we get:
P(interior) = 3x10^-7 watts/cm^3 x 1.41x10^27 cm^3 = 4.23x10^20 watts
The power emitted by the star's surface can be calculated using the formula for the surface area of a sphere:
A = 4πr²
Substituting r = 7x10^8 cm, we get:
A = 4π(7x10^8)^2 ≈ 6.16x10^18 cm^2
Multiplying this area by the power emitted per square centimeter, we get:
P(surface) = 6,000 watts/cm² x 6.16x10^18 cm^2 = 3.70x10^22 watts
We can see that the power emitted by the star's surface is much greater than the power generated by its interior.
b) Following the same process as in part (a), we get:
V = (4/3)π(5x10^12)³ = 5.24x10^38 cm³
P(interior) = 3x10^-7 watts/cm^3 x 5.24x10^38 cm^3 = 1.57x10^32 watts
A = 4π(5x10^12)^2 ≈ 3.14x10^26 cm²
P(surface) = 6,000 watts/cm^2 x 3.14x10^26 cm^2 = 1.88x10^30 watts
Again, we see that the power emitted by the star's surface is much greater than the power generated by its interior. However, the difference between the two quantities is much smaller in this case compared to the previous case.
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Miguel needs to memorize words on a vocabulary list for Russian class. He has memorized 36 of the words, which is three-fourths of the list. How many words are on the list?
After answering the presented questiοn, we can cοnclude that equatiοn Therefοre, there are 144 wοrds οn the vοcabulary list.
What is equatiοn?A mathematical equatiοn is a fοrmula that cοnnects twο statements and denοtes equivalence with the equals symbοl (=). An equatiοn is a mathematical statement that shοws the equality οf twο mathematical expressiοns in algebra. In the equatiοn 3x + 5 = 14, fοr example, the equal sign separates the variables 3x + 5 and 14.
A mathematical fοrmula describes the cοnnectiοn between the twο sentences that οccur οn οppοsite sides οf a letter. The symbοl and the single variable are frequently the same. As in 2x - 4 Equals 2, fοr instance.
1/4 x = tοtal number οf wοrds Miguel has nοt memοrized
1/4 x = x - 36
x/4 = 36
x = 144
Therefοre, there are 144 wοrds οn the vοcabulary list.
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11 of 20
What is the Order of Operations in Sheets?
Answer:
You may have experience working with formulas that contain only one operator, such as 7+9. More complex formulas can contain several mathematical operators, such as 5+2'8. When there's more than one operation in a formula.
Step-by-step explanation:
Don't ask i just know
The circle below is centered at the point (-3.5, 6) and has a radius of length 1.6. Write the equation for the circle.
Answer:
(x – 3.5)^2 + (y +6)^2 = 1.6^2
Step-by-step explanation:
(x – h)^2 + (y – k)^2 = r^2 is the equation of a circle
plug the radius in for r
switch the signs of the center points and plug them in for h and k
Calculate the cross product (+)×(5+4)
assuming that
×=⟨1,1,0⟩,×=⟨0,3,1⟩,×=⟨2,−1,1⟩
The cross product of (+) and (5+4) is approximately ⟨-0.362, 0.536, 0.489⟩.
To calculate the cross product (+)×(5+4)We need to use the vector cross product formula:
a × b = |a| |b| sin(θ) n
Where
a and b are the two vectors being multiplied, |a| and |b| are their magnitudesθ is the angle between themn is a unit vector perpendicular to both a and b (in the direction determined by the right-hand rule)Using the given values of ×, we have:
(+) × (5+4) = ⟨1, 1, 0⟩ × ⟨5, 4, 0⟩
= |⟨1, 1, 0⟩| |⟨5, 4, 0⟩| sin(θ) n
Where θ is the angle between ⟨1, 1, 0⟩ and ⟨5, 4, 0⟩. To find θ, we can use the dot product formula:
a · b = |a| |b| cos(θ)
⟨1, 1, 0⟩ · ⟨5, 4, 0⟩ = |⟨1, 1, 0⟩| |⟨5, 4, 0⟩| cos(θ)
1(5) + 1(4) + 0(0) = √2 √41 cos(θ)
9 = 2√41 cos(θ)
cos(θ) = 9/(2√41)
θ ≈ 20.11 degrees
Now we can plug in the values to find the cross product:
(+) × (5+4) = |⟨1, 1, 0⟩| |⟨5, 4, 0⟩| sin(20.11) n
= √2 √41 sin(20.11) n
= (2/√41) ⟨-2sin(20.11), 3sin(20.11), 2√2cos(20.11)⟩
= ⟨-0.362, 0.536, 0.489⟩
Therefore, the cross product of (+) and (5+4) is approximately ⟨-0.362, 0.536, 0.489⟩.
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please fill in the blanks
The probability that the next flip results in a head is 0.77.
How to calculate the probabilityIn statistics, probability refers to the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur. For instance, if the probability of an event A is 0.7, then there is a 70% chance that A will occur, and a 30% chance that it will not occur.
In the toss of coin 100 times, one gets 77 heads and 23 tails. The probability that the next flip results in a head will be:
= 77/100
= 0.77
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Which of the following is a solution to this inequality?
y<2/3x+2
(0, 3)
(−3, 1)
(3, 5)
(1, 2)
Answer:
(d) (1, 2)
Step-by-step explanation:
You want to know which of the given points satisfies the inequality.
GraphWe find it easiest to plot the given points on a graph of the solution. This shows us that (1, 2) is a solution to the inequality. (It lies in the solution area.)
__
Additional comment
Another way to choose the answer is to try each of the points in the inequality.
If you can visualize the boundary line (without plotting it) as a line with positive slope and a y-intercept of 2, you can more readily reject the first choice and accept the last choice. (0, 3) is above the y-intercept, and (1, 2) is to the right of it (in the solution space).
You may also recognize the x-intercept will be -3, so the second choice lies above the boundary line.
ΔQRS is an isosceles triangle. What is the length of RT¯¯¯¯¯
R
T
? Round to the nearest hundredth. Enter your answer in the box.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22[/tex]
K
You randomly select one card from a 52-card deck. Find the probability of selecting a four or a six.
The probability is. (Type an integer or a fraction. Simplify your answer.)
Answer:
2/13
Step-by-step explanation:
There are 8 cards in a standard 52-card deck that are either fours or sixes (four fours and four sixes).
Therefore, the probability of selecting a four or a six is:
P(selecting a four or a six) = 8/52 = 2/13
So the probability is 2/13.
A total of 100 people went to the
movies. A ticket cost $4 for adults and
$2 for children. The total sales
amounted to $276. How many children
and adults attended the movies?
Using a system of equations, the number of children and adults who attended the movies is as follows:
Children = 62Adults = 38.What is a system of equations?A system of equations is two or more equations solved concurrently.
A system of equations is also known as simultaneous equations.
The total number of people who went to the movies = 100
The unit cost of adult tickets = $4
The unit cost of children tickets = $2
The total sales = $276
Let the number of children who attended the movies = x
Let the number of adults who attended the movies = y
Equations:x + y = 100 ... Equation 1
2x + 4y = 276 ... Equation 2
Multiply Equation 1 by 2:
2x + 2y = 200 ... Equation 3
Subtraction Equation 3 from Equation 2:
2x + 4y = 276
-
2x + 2y = 200
2y = 76
y = 38
Substitute y = 19 in equation 1:
x + y = 100
x + 38 = 100
x = 62
Check in Equation 2:
2x + 4y = 276
2(62) + 4(38) = 276
124 + 152 = 276
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In order to pass your final assessment you must answer 75% of the questions correctly.There are 84 questions then I must get how many questions correct to pass
Answer:
63 answers
Hope this helps :p
The total number of questions to be answered correctly so that 75% of answers are correct is 63.
∵ To pass the assessment, the percentage of questions to be answered correctly = 75.
That means, for every 100 questions, the number of correct answers required = 75
∴ For 1 question, the number of correct answers required= 75/100
=3/4
But, the total number of questions in the assessment = 84
∴ For 84 questions, the number of correct answers required = 3/4×84
= 63
Hence, the total number of questions to be answered correctly so that 75% of answers are correct is 63.
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Find the lateral area of the cone in terms of π.
15π cm2
18π cm2
21π cm2
12π cm2
Answer:
[tex]12\pi \: {cm}^{2} [/tex]
Step-by-step explanation:
Given:
A cone
r (radius) = 3 cm
h (height) = 4 cm
Find: A (lateral) - ?
[tex]a(lateral) = \pi \times r \times l[/tex]
[tex]a(lateral) = \pi \times 3 \times 4 = 12\pi \: {cm}^{2} [/tex]
Suppose a researcher is trying to understand whether people who purchase fast-food hamburgers would be willing to pay more if the hamburger comes with a free whistle. Prior research suggests the mean amount customers say they are willing to pay for a hamburger is μ = 3.68 and σ = 0.70. The researcher plans to conduct a study very similar to the prior research by selecting a sample of customers and asking them how much they are willing to pay for the hamburger. Before asking, however, she will tell the customer about the free whistle that will come with the hamburger. The researcher’s null hypothesis is that the mean amount the customers are willing to pay when they are told about the free whistle is no different than the amount customers are willing to pay when they are not told they will receive a free whistle. The researcher’s sample of 49 customers has a sample mean of M = 4.04. The test statistic for this sample mean is 3.60. Using a significance level of α = .05, which of the following is the most appropriate statement of the result?
a. Telling customers they will receive a free cookie with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.68, p < .05.
b. Telling customers they will receive a free cookie with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 4.04, p > .05.
c. Telling customers they will receive a free cookie with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
d. Telling customers they will receive a free cookie with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05
Compute the estimated Cohen’s d to measure the size of the treatment effect.
Note: Cohen’s d is always reported as a positive value and reflects the proportion of the standard deviation that is affected by the treatment.
Estimated Cohen’s d =
Using Cohen’s criteria, the estimated Cohen’s d indicates that telling customers they will receive a free whistle is associated with a in the amount they are willing to pay for the hamburger.
The correct answer is option c: Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
What is standard deviation?A statistical measure known as the standard deviation depicts how variable or dispersed a set of data is. It is determined by taking the square root of the variance, which is the sum of the squared deviations from the data set mean. While a large standard deviation suggests that the data points are more dispersed, a small standard deviation suggests that the data points tend to be close to the mean. It can be used to assess the variability between different data sets and is frequently used as a gauge of a data set's consistency or reliability.
Given, level of significance = 0.05.
n = 49 and sample > 30
Thus, using z-score we have:
z = 4.04 - 3.68 / (0.70/7) = 3.60
Now, p-value = 0.000318
Now, for P < 0.05 we have:
cohens D = 4.04 - 3.67 / 0.70 = 0.51
This shows a medium increase.
Hence, the correct answer is option c: Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
The estimated Cohen’s d is given as:
Cohen’s d = (M - μ) / σ
The sample standard deviation is not given, so we cannot calculate the exact value of Cohen's d.
The sample standard deviation will determine the estimated Cohen's d in this situation, although if it is greater than 0.2, it might be regarded as having a small effect size.
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
After answering the presented questiοn, we can cοnclude that Because equatiοn the mean is nοt included in the bοx plοt descriptiοns, it cannοt be utilized tο cοmpare the twο drive-thrush.
What is equatiοn?A mathematical equatiοn is a fοrmula that cοnnects twο statements and denοtes equivalence with the equals symbοl (=). An equatiοn is a mathematical statement that shοws the equality οf twο mathematical expressiοns in algebra. In the equatiοn 3x + 5 = 14, fοr example, the equal sign separates the variables 3x + 5 and 14.
Because its bοx plοt indicates a wider variety οf wait times, Burger Quick generally has a lοnger wait time than Super Fast Fοοd. The number line οn the Burger Quick bοx extends frοm 9.5 tο 24, hοwever the number line οn the Super Fast Fοοd bοx οnly runs frοm 8.5 tο 15.5.
Alsο, the median οf Burger Quick (15.5) is higher than the median οf Super Fast Fοοd (15.2). (12). Because the mean is nοt included in the bοx plοt descriptiοns, it cannοt be utilized tο cοmpare the twο drive-thrus.
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11
k
The model below is shaded to represent an expression.
Which expression represents the model?
1 2
3 x 5
A
B
D
1 5
3x2
2
3x5
5
3x 2
The expression which represents the model is (3 × 2/5). The Option C is correct.
What does a model means?A modeling refers to the process of creating a representation of a real-world scenario to make a prediction or provide insight.
In the given question, it can be observed that the model contains 10 parts in total with a division of 5 each into 2 parts.
Since the division of 2 is made thrice, it gives us:
3 × 2/5
Hence, this makes the third option (3 × 2/5) the correct one.
Note: The full question is attached as picture as below.
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A desk is on sale for $119, which is 65% less than the regular price.
Answer:
320 would be the regular price
Step-by-step explanation:
naina made a 10 layer multi strand ornament for her friend Diana. She used 45 beads for the first layer, 42 beads in the 2nd layer and 39 beads in the third layer. how many total beads did naina use to complete the ornament
Answer:
To find the total number of beads Naina used to complete the ornament, we need to sum the number of beads in each layer.
Total number of beads = 45 + 42 + 39 + ... (continue the pattern until the 10th layer)
Notice that the number of beads in each layer decreases by 3. We can use arithmetic series formula to find the sum of the beads in all 10 layers:
S = (n/2) x (a + l)
where S is the sum, n is the number of terms, a is the first term, and l is the last term.
Here, a = 45, l = 18 (since the 10th layer will have 18 beads), and n = 10 (since there are 10 layers). Thus, we have:
S = (10/2) x (45 + 18) = 5 x 63 = 315
Therefore, Naina used a total of 315 beads to complete the ornament.
Answer:
The answer to your problem is, 1260
Step-by-step explanation:
Well we know she made 10 “ strand ornaments “ for each layers we would need to add;
45 + 42 + 39
= 126
We would actually then need to multiply it by 10. Shown:
126 × 10
= 1260
Thus the answer to your problem is, 1260
Question 6(Multiple Choice Worth 1 points)
(08.03 MC)
A portion of the quadratic formula proof is shown. Fill in the missing reason.
Statements Reasons
ax2 + bx + c = 0 Given
ax2 + bx = −c Subtract c from both sides of the equation
x squared plus b over a times x equals negative c over a Divide both sides of the equation by a
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus the quantity b over 2 times a squared Complete the square and add the quantity b over 2 times a squared to both sides
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus b squared over 4 times a squared Square the quantity b over 2 times a on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a end quantity squared equals negative 4 times a times c over 4 times a squared plus b squared over 4 times a squared Find a common denominator on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation
quantity x plus b over 2 times a end quantity squared equals b squared minus 4 times a times c all over 4 times a squared ?
Rewrite the perfect square trinomial as a binomial squared on the left side of the equation
Take the square root of both sides of the equation
Multiply both sides of the equation by 2
Square the left side of the equation
Quantity x plus b over 2 times a end quantity squared equals b squared minus 4 times a times c all over 4 times a squared
What is the missing statement?
Rewrite the perfect square trinomial as a binomial squared on the left side of the equation
quantity x plus b over 2 times a end quantity squared equals b squared minus 4 times a times c all over 4 times a squared
Take the square root of both sides of the equation
x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c all over 2 times a
Multiply both sides of the equation by 2
2 times a times quantity x plus b over 2 times a end quantity equals plus or minus the square root of b squared minus 4 times a times c
Simplify
x plus b over 2 times a equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a
Square the left side of the equation is not necessary for the proof of the quadratic formula.
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Please help !!!!!!!!!
The expression can be said to be equivalent because they could be simplified to give the same result.
What are equivalent expressions?Equivalent expressions are two or more mathematical expressions that have the same value for all values of the variables involved. In other words, if you substitute the same values for the variables in two different expressions that are equivalent, you will get the same result.
Thus we can see that; 1/2x^3(8x + 10x^6) is equivalent to x^4(5x^4 + 4) as shown
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Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.
Answer:
Since Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour, we can use the following system of inequalities to represent the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal:
3w + 6r ≥ 36
3w + 6r ≤ 90
The first inequality states that the total number of miles Keitaro walks and runs must be at least 36 miles per month. The second inequality states that the total number of miles Keitaro walks and runs must not exceed 90 miles per month.
So I need to fill out a proof of income for food stamps and I need to write down how much I made for each of these months jan feb and March now I can't go under the amount of gross income which in total is 2495 with the net being 1920 so what amount would I put to be over just a little of that for each month
Answer:
Step-by-step explanation:
To calculate how much you need to earn each month (January, February, and March) to be just over the gross income of $2495, you can divide that amount by 3 (since there are 3 months) and then add a small amount to ensure that you are over the limit. Here's how you can do that:
1) Divide the gross income by 3:
$2495 ÷ 3 = $831.67 (rounded to the nearest cent)
2) Add a small amount to each month's income to ensure that you are over the limit. You could add $1 or $5, for example. Let's say you add $5 to each month:
January: $831.67 + $5 = $836.67
February: $831.67 + $5 = $836.67
March: $831.67 + $5 = $836.67
So for each month, you should report an income of $836.67 (or whatever amount you calculated using the method above) to ensure that you are over the gross income limit of $2495.
find the relationship of the rate change (slope) and initial value when x=0 (y intercept) between x and y for the following table of values of x the independent variable and y the dependent variable also find the equation of the line in slope intercept form y=mx+b please show and explain your work
The rate of change is -2 and the initial value when x=0 (y intercept) is -1.
An equation of this line in slope-intercept form is y = -2x - 1.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope or rate of change of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (3 - 5)/(-1 + 2)
Slope (m) = -2/1
Slope (m) = -2
At data point (-2, 5) and a slope of -2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -2(x + 2)
y - 5 = -2x - 4
y = -2x - 1
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Help me with this question
Answer:27.5 i hope you really like this answer i hope its right too
Answer:
46
Step-by-step explanation:
You want to know the number of regular pentagonal prism marshmallows that can be covered with 1.5 L of chocolate if each cm² takes 0.5 mL. The base area is 7 cm², and each rectangular face is 2 cm by 5 cm.
AreaThe area of each marshmallow is the sum of the areas of the 2 bases and 5 faces. Each face is a 2 cm by 5 cm rectangle, so has an area of ...
A = LW
A = (5 cm)(2 cm) = 10 cm²
The bases each have an area of 7 cm², so the total area is ...
total area = base area + face area
total area = 2 × 7 cm² + 5 × 10 cm² = 64 cm²
ChocolateEach cm² takes 0.5 mL of chocolate to cover it, so the chocolate required for one marshmallow is ...
(0.5 mL/cm²)(64 cm²) = 32 mL
1.5 L of chocolate is 1500 mL, so the number that can be covered is ...
(1500 mL)/(32 mL/marshmallow) = 46 7/8
Kaitlyn can completely cover 46 marshmallows with the chocolate she has.
sinusodial math equations
f. The height of the endpoint of the minute hand above the bookshelf at 6:00 am is 23 cm. g. when θ = 160 is -4.33 cm. h. g(θ) is 10. i. k = 150.
Describe Function?A function is a mathematical concept that describes the relationship between two sets of numbers or values, called the domain and the range. It assigns to each value in the domain a unique value in the range. The domain is the set of all possible input values, while the range is the set of all possible output values.
A function can be represented by an equation, a graph, or a table of values. The equation of a function typically has a variable, often denoted as x, that represents the input or independent variable, and a formula that expresses how the input is transformed to obtain the output or dependent variable, often denoted as y.
f. At 6:00 am, the minute hand is pointing directly up, so the angle rotated by the minute hand from 6:00 am is θ = 0. Plugging this into the function h(θ) = 10 cosθ + 13, we get:
h(0) = 10 cos(0) + 13 = 23
So, the height of the endpoint of the minute hand above the bookshelf at 6:00 am is 23 cm.
g. To find the height of the endpoint of the hour hand above the bookshelf when θ = 160, we need to convert θ to the angle rotated by the hour hand from 6:00 am. Since the hour hand rotates 30 degrees for every hour, or 0.5 degrees per minute, the angle rotated by the hour hand from 6:00 am is 30(5) + 0.5(0) = 150 degrees.
So, we need to find g(150), which is:
g(150) = -10 cos(150/12) + 13 = -4.33
Therefore, the height of the endpoint of the hour hand above the bookshelf when θ = 160 is -4.33 cm.
h. The amplitude of g(θ) is the absolute value of the coefficient of the cosine function, which is 10. So, the amplitude of g(θ) is 10.
i. The endpoints of the minute hand and hour hand meet when they are pointing in the same direction, so the angle rotated by the minute hand from 6:00 am must be a multiple of 30 degrees. To find the smallest possible value of k, we need to find the smallest multiple of 30 that is greater than or equal to 150 (the angle rotated by the hour hand from 6:00 am). This is 30(5) = 150.
So, the smallest possible value of k is when the minute hand has rotated 150 degrees from 6:00 am, which is at 5:00 am and 30 seconds. Therefore, k = 150.
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