To find the total number of sheep in the flock where 2 out of 5 are white and there are 8 more black than white sheep, we set up a ratio and solve for the number of white sheep (W), which is 16. We then determine the number of black sheep (B) to be 24, leading to a total of 40 sheep.
Explanation:The subject of the question is mathematics, and it appears to be at the middle school level. The task involves determining the total number of sheep given that 2 out of 5 are white and there are 8 more black sheep than white. Let's define the variables: W for white sheep and B for black sheep. From the statement, we have the ratios W/B = 2/3 because for every 2 white sheep, there are 3 black sheep which are proportionally 5 sheep in total (2+3=5), and we have the relationship B = W + 8 because there are 8 more black than white sheep. Using these equations, we can solve for W and B.
From the ratio W/B = 2/3, we can express B as B = 3/2 * W.Replace B in the second equation with 3/2 * W:Therefore, the total number of sheep in the flock is 40.
Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below.
Answer:
581.25
Step-by-step explanation:
Use the formula for when the last term is unknown. It is [tex]s_{n} = \frac{a_{1} - a_{1} (r)^{n} }{1-r}[/tex].
For this equation [tex]s_{n}[/tex] (sum of the numbers)= [tex]s_{5}[/tex], [tex]a_{1}[/tex] (amount of first term) = 300, r (ratio)= .5, and n (number of terms) = 5. Knowing this, we plug them into the equation. It would look like: [tex]s_{10} = \frac{300 - (300)(0.5)^{5} }{1-0.5}[/tex].
First, we solve the exponents. 0.5 to the fifth power = .03125. Now multiply it by the nearest number in parentheses, which is 300. You should get 9.375.
Now, subtract that from 300. 300 - 9.375 = 290.625. Your numerator is 290.625.
Simplify your denominator. 1 - 0.5 = 0.5.
Divide.
[tex]\frac{290.625}{0.5} = 581.25[/tex]
581.25
I tried to make sure there were no typos! Please let me know if I missed something :)
Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why ABC LMN?
Answer:
D, E, and F
Step-by-step explanation:
D. SAS can be used, side-angle-side. The angle is the right angle in both and right angles always are congruent since they can only measure 90 degrees. The heights of both triangles are marked with the same number of slashes, so they are congruent; likewise, the bases are marked with the same number of slashes, so they are congruent. Since the angle is between the sides, or included, this is SAS.
E. HL can also be used since the hypotenuses of both triangles are marked with the same number of slashes, they are congruent. We already decided the legs of both were congruent to each other.
F. LL (which is also exactly the same as SAS) can also be used since we already decided that the legs in both triangles are congruent.
More information about the diagram and angles and sides is needed to determine the congruence theorems or postulates that can be applied.
Explanation:In order to determine which congruence theorems or postulates can be used to prove that triangles ABC and LMN are congruent, we need more information about the diagram and the given angles and sides. Without that information, it is not possible to determine which congruence theorems or postulates can be applied.
Anyone knows the answer
How is the graph y=7x^2+4 different from the graph of y=7x^2
kevin walked 3/4 of a mile in 12 minutes. assuming he walked at a constant speed the entire time, which expression can be used to determine the distance he walked each minute?
Answer:
We know that Kevin moved at a constant speed, so his movement can be model by:
[tex]d=st[/tex]
Where [tex]d[/tex] is distance, [tex]s[/tex] is speed and [tex]t[/tex] is time.
So, we can find the speed first, to then find the expression of the distance at any time:
[tex]s=\frac{d}{t}=\frac{\frac{3}{4}mi}{12min}\\s=\frac{3}{48}mi/min\\s=\frac{1mi}{16min}[/tex]
The ratio of his movement is 1 miles each 16 minutes.
Then, the distance at any minute would be:
[tex]d=\frac{1}{16}t[/tex]
This expression model the entire movement of Kevin, because it gives the distance he traveled at any minute.
For example, the first minute, Kevin covered a distance of:
[tex]d=\frac{1}{16}(1)=0.063 miles[/tex]
So, we could say that he travels 0.063 miles per minute.
WILL MARK BRAINLYIST!
Which postulate or theorem proves that △RMN and △QPN are congruent?
A. AAS Congruence Theorem
B. SSS Congruence Postulate
C. ASA Congruence Postulate
D. SAS Congruence Postulate
Answer: C. ASA Congruence Postulate proves that △RMN and △QPN are congruent.
Given: △RMN and △QPN where RN=NQ and ∠R=∠Q
To prove: △RMN ≅△QPN
Proof:- In △RMN and △QPN
∠R=∠Q............[given]
RN=NQ............[given]
∠RNM=∠PNQ............[vertically opposite angles]
∴△RMN ≅△QPN [by ASA Congruence Postulate ]
Therefore,C. is the right answer. ASA Congruence Postulate proves that △RMN and △QPN are congruent.
ASA Congruence Postulate states that is two angles and the included side is equal to the two angles and the included side of the other triangle, then the triangles are said to be congruent.
Hank is painting his grandfather's fence. He painted 40 linear feet in 85 minutes. He still has 360 linear feet to paint. His cousins, Sam and Alex, come to help. Sam paints twice as fast as Hank, and Alex paints half as fast as Hank. Find the constant of proportionality for the fence painting rate of Hank, Sam, and Alex combined.
HELP PLEASE!!!!!!!!!
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We are given that the suitcase is 24 inches long and 18 inches high. Assuming a regular rectangular shape, the diagonal can be calculates using Pythagorean theorem, that is:
diagonal^2 = 24^2 + 18^2
diagonal^2 = 900
diagonal = 30 inches
Answer:
Step-by-step explanation:
If the discriminant is 16 in a quadratic equation what is true about its solutions
If the discriminant in a quadratic equation is 16, a positive number, then the quadratic equation will have two distinct real solutions.
Explanation:In mathematics, particularly in quadratic equations, the discriminant plays a vital role in determining the nature of the solutions. The discriminant in a quadratic equation is the part under the square root in the quadratic formula, and it is usually represented by the symbol Δ (Delta). The quadratic formula is given by x = [-b ± sqrt(Δ)] / 2a. Now, if the discriminant is 16 (a positive number), then the quadratic equation will have two distinct real solutions. This is because the square root of a positive number yields two real numbers (one positive and one negative) which provide the two solutions when substituted back into the quadratic formula.
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11x+7y=49 in y=mx+b format
Figure out the pattern, fill in the blank.
The number to fill the given blank is 384.
We need to figure out the pattern from the number sequence.
What is the pattern in the number sequence?A number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers.
From the given figure we can see that the pattern following the sequence is as follows:
From the bottom blocks to the block just above that it is multiplied by two numbers in the bottom blocks to get the number in the corresponding top block.
That, 6×2=12, 2×2=4, 2×1=2, 12×4=48, 4×2=8 and 48×8=384.
Therefore, the number to fill the given blank is 384.
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simplify 1,000^8=10^w
The value of [tex]w[/tex] is [tex]24[/tex].
Given:
The equation is:
[tex]1000^8=10^w[/tex]
To find:
The value of [tex]w[/tex].
Explanation:
We have,
[tex]1000^8=10^w[/tex]
[tex](10^3)^8=10^w[/tex]
[tex]10^{24}=10^w[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
On comparing the exponents of the same bases, we get
[tex]24=w[/tex]
Therefore, the value of [tex]w[/tex] is [tex]24[/tex].
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Which of the following is something you need to think about throughout unit 5 ?
A the independent reading
B the skills for arguments
C the writing prompt
D the opinions you have
Answer:
B the skills for arguments
Step-by-step explanation:
gurl just read the lesson lol
and it's not the opinions you have other person is incorrect
A recipe asks for 6 1/4 cups of flour. How many cups of flour are needed to make 1/2 of a recipe
the answer is 3 1/8!
sorry if this is really late,,, hope this helps <3
One hundred tickets, numbered 1,2,3, ,100, are sold to 100 different people for a drawing. four different prizes are awarded, including a grand prize (a trip to tahiti).
There are four questions related to this: how many number of ways are there to award the prizes if:
a) There are no restrictions? If k unalike awards are there for n people and no person can get more than one prize then there are: This leads to 100 × 99 × 98 × 97 = 94109400100 × 99 × 98 × 97 = 94109400 ways in your case where n=100 k=4.
b)The person holding ticket 47 wins the grand prize? After handing out the grand prize there are k=3 different rewards left for n = 99 persons. Apply the same formula. Answer: 941094941094
c) The person holding ticket 47 wins one of the prizes? 4 times case because there are 4 likelihoods when it comes to the rewards that can be won by person 47. Answer: 37643763764376
d) The person holding ticket 47 does not win a prize? k=4 and n =99.
Person 4747 is left out. Answer: 9034502490345024
e) The person holding ticket 19 and 47 both wins prize? First gave out a
prize to 47. There are 4 possibilities. Then give out a prize
to 19. There are 3 likelihoods. Then the other prizes are gave
out: k=2 and n=98. Lastly you come to 4 × 3 × 98 × 97 =1140724
× 3 × 98 × 97 = 114072 possibilities.
Scott bought 6 pounds of flour for $4 . how many dollars did he pay per pound of flour?
Final answer:
Scott paid approximately $0.67 per pound of flour, calculated by dividing the total cost of $4 by the total weight of 6 pounds.
Explanation:
The student asked: Scott bought 6 pounds of flour for $4. How many dollars did he pay per pound of flour?
To figure out the cost per pound of flour, you need to divide the total cost by the number of pounds.
Step-by-Step Calculation:
Write down the total cost of the flour, which is $4.
Write down the total weight of the flour, which is 6 pounds.
Divide the total cost by the total weight to find the cost per pound: $4 ÷ 6 pounds
The result is approximately $0.67 per pound.
Scott paid approximately $0.67 for each pound of flour.
does anyone know this?
Find the distance between points (1,3) and (5,7) round the answer to two decimal points
An item has a listed price of $65. If the sales tax rate is 5%, how much is the sales tax in dollars?
The amount of sales tax in dollars is $3.25.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Percentage is usually denoted by the symbol '%'.
Given that,
An item has a listed price of $65 and the sales tax rate is 5%.
Listed price of an item = $65
Rate of sales tax = 5%
To calculate the amount of sales tax, we have to calculate the amount of 5% of the listed price which is $65.
Amount of sales tax = 5% of $65
= 5% × 65
= (5/100) × 65
= 0.05 × 65
= 3.25
Hence the amount of sales tax for the item is $3.25.
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A rectangular shaped desk has a length of 25 inches and a width of 18 inches. A desk with a similar shape has a length of 60 inches. What is the width of this desk?
Answer:
43.2 in
Step-by-step explanation:
I took it
If rectangular shaped desk has a length of 25 inches and a width of 18 inches. A desk with a similar shape has a length of 60 inches. then its width will be 43.2 inches.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
A rectangular shaped desk has a length of 25 inches and a width of 18 inches
A desk with a similar shape has a length of 60 inches. x is the width of this desk
We need to find the value of x.
Let us formulate a equation.
25/18=60/x
Apply cross multiplication
25x=18(60)
25x=1080
Divide both sides by 25.
x=43.2
Hence if a desk with a similar shape has a length of 60 inches it will have 43.2 inches of width.
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Which of the following are steps in practical problem solving? Assign an identifying variable to the quantity to be found. Make a guess at the value of the variable. Write a sentence stating conditions placed on the quantity. Check if the value is correct. Solve the sentence for the variable.
Answer:
1. Assign an identifying variable to the quantity to be found.
2. Write a sentence stating conditions placed on the quantity.
3. Solve the sentence for the variable.
Which substance is a heterogeneous mixture?
Cereal
Silver
Nickel
Shampoo
Cereal is a heterogeneous mixture. Because it is not uniformly mixed together since it has a variety of components. Option A is correct.
What is a heterogeneous mixture?When the composition of a mixture is not constant throughout the mixture, the mixture is said to be heterogeneous. A variety of ingredients make up vegetable soup. Each mouthful of soup will have variable proportions of the soup's various veggies and other ingredients.
Given that the ingredients are visible and diverse, it is unmistakably cereal. The remaining choices, whether they be mixes or natural components, are homogenous since the contents blend well.
Because it contains a variety of unbalanced ingredients like flakes, berries, and clusters, cereal is a wonderful illustration of a heterogeneous mixture. A homogeneous mixture is one in which the constituent parts are thoroughly combined, as seawater.
Thus, Cereal is a heterogeneous mixture. Because it is not uniformly mixed together since it has a variety of components. Option A is correct.
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Tickets for the baseball games were $2.50 for general admission and 50 cents for kids. If there were six times as many general admissions sold as there were kids tickets, and the total receipts were $7750, how many of each type of ticket were sold?
The number of tickets sold of each type is required.
Number of general tickets sold is 3000 and kids tickets is 500.
The cost of general tickets is $2.5
Cost of kids tickets is $0.5
Number of general tickets sold = x
Number of kids tickets sold = y
Total value of tickets sold = $7750
Now,
[tex]x=6y[/tex]
[tex]2.5x+0.5y=7750\\\Rightarrow 2.5(6y)+0.5y=7750\\\Rightarrow 15.5y=7750\\\Rightarrow y=\dfrac{7750}{15.5}\\\Rightarrow y=500[/tex]
[tex]x=6\times 500=3000[/tex]
Number of general tickets sold is 3000 and kids tickets is 500.
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The longer leg of a right triangle is 4m longer than the shorter leg. the hypotenuse is 8m longer than the shorter leg. find the side lengths of the triangle.
The lengths are 12 m, 16 m, and 20 m.
What is a hypotenuse in the triangle?In a right triangle, the hypotenuse is the longest aspect, an "contrary" aspect is the one throughout from a given attitude, and an "adjacent" aspect is subsequent to a given perspective.
How do I discover the hypotenuse of a proper triangle?The hypotenuse is opposite to the right perspective and may be solved by means of using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c, Pythagoras' theorem states that: a² + b² = c². To clear up for c, take the rectangular root of both aspects to get c = √(b²+a²).
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Multiply and simplify if possible square root of 6 multiply square root 2
To multiply square roots, you multiply the numbers under the root (the radicands) and then take the square root of that result. So, square root of 6 multiplied by square root of 2 equals the square root of 12.
Explanation:
The student's question requires multiplication of square roots. When multiplying square roots, we multiply the numbers under the roots (i.e., the radicands) and then compute the square root of that result.
So, to solve √6 * √2, we multiply the radicands (6 * 2) to get 12. Hence, √6 * √2 = √12. In some cases, we can simplify this further by factoring the radicands into the product of two numbers, where one of those numbers is a perfect square. However, 12 is already a simplified form, so the final answer will be √12.
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The length of the base of an isosceles triangle is 15. what is the range of possible lengths l for each leg?
The range of possible lengths for each leg of the triangle will be greater than 7.5.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The two triangular legs and their opposing angles are congruent in an isosceles triangle.
For a triangle, the sum of the two sides should be greater than the longest side of the triangle.
The length of the foundation of an isosceles triangle is 15.
Let the isosceles sides of the triangle be 'x'. Then the inequality is given as,
x + x > 15
2x > 15
x > 7.5
The range of possible lengths for each leg of the triangle will be greater than 7.5.
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Your regular pay of $67, plus tips, came up to $182.50. How much were the tips? Be sure to write your answer in dollars and cents. $115.50 $67 $182.50 Not enough information
Answer:
115.50
Step-by-step explanation:
I took the test
The table shows the growth of a type of bacteria. How many bacteria will be present after 6 hours? [Use an exponential regression curve.]
Answer:
3404
Step-by-step explanation:
The mass of a pencil is 5.44 g. The mass of a crayon is 2.145 g. How much greater is the mass of the pencil than the mass of the crayon?
Answer:
The mass of a pencil is 3.295 greater than the mass of the crayon.
Step-by-step explanation:
Consider the provided information.
The mass of a pencil is 5.44 g. The mass of a crayon is 2.145 g.
We need to find how much greater is the mass of the pencil than the mass of the crayon?
To find this simply subtract the mass of a crayon from mass of a pencil.
5.44-2.145
This can be written as:
5.440
-2.145
3.295
Hence, the mass of a pencil is 3.295 greater than the mass of the crayon.
The mass of the pencil is 3.295 grams greater than the mass of the crayon.
How did we get the value?To find out how much greater the mass of the pencil is compared to the crayon, we need to subtract the mass of the crayon from the mass of the pencil.
Mass of the pencil = 5.44 g
Mass of the crayon = 2.145 g
Mass difference = Mass of the pencil - Mass of the crayon
= 5.44 g - 2.145 g
= 3.295 g
Therefore, the mass of the pencil is 3.295 grams greater than the mass of the crayon.
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