Answer:
Ariel will make a bigger batch.
Step-by-step explanation:
Scott- Every 2 cups Almonds = 3 cups raisins
so 6 cups almonds = 9 cups raisins
6+9= 15
Scott's batch- 15 cups
Ariel- Every 3 cups Almonds = 5 cups sunflower seeds
so 6 cups almonds = 10 cups sunflower seeds
6+10= 16
Ariel's batch- 16 cups
16 > 15 so Ariel's is bigger.
Ariel makes the larger batch of snack mix
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Equation for Scott :
Number of cups of Almonds = 2 cups
Number of cups of Raisins for 2 cups of almonds = 3 cups
Number of cups of almonds = 6 cups
Number of cups of raisins for 6 cups of almonds = 3 x 3
= 9 cups
So , total number of cups by Scott =
Number of cups of almonds + Number of cups of raisins for 6 cups of almonds
Total number of cups by Scott = 6 + 9 cups
The batch of snack mix by Scott has 15 cups
Equation for Ariel :
Number of cups of Almonds = 3 cups
Number of cups of sunflower seeds for 3 cups of almonds = 5 cups
Number of cups of almonds = 6 cups
Number of cups of raisins for 6 cups of almonds = 5 x 2
= 10 cups
So , total number of cups by Ariel =
Number of cups of almonds + Number of cups of sunflower seeds for 6 cups of almonds
Total number of cups by Ariel = 6 + 10 cups
The batch of snack mix by Ariel has 16 cups
Therefore , the batch mix of snack by Ariel is more than the batch mix of snack by Scott
Hence , Ariel makes the larger batch
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Please help last question and I don’t understand
Answer: 282.74
Step-by-step explanation:
V= pi r^2 h = pi * 3^2 * 10 = 282.74
Researchers at the National Cancer Institute re- leased the results of a study that investigated the effect of weed-killing herbicides on house pets. They examined 827 dogs from homes where an herbicide was used on a regular basis, diagnosing malignant lymphoma in 473 of them. Of the 130 dogs from homes where no herbicides were used, only 19 were found to have lymphoma.a) What’s the standard error of the difference in the two proportions? b) Construct a 95% confidence interval for this difference. c) State an appropriate conclusion.
Answer:
A)The Standard error for difference in proportion is 0.0354
B)The Confidence interval with 95 % for difference in proportion is (0.356 ,0.495)
C)The conclusion is that proportion of herbicides and no herbicides and having them diagnosed with malignant lymphoma is between 35.6 % and 49.5 % And higher than the proportion to pets in homes where no pesticides were used.
Step-by-step explanation:
Given:
Total dogs which are herbicide =827=n1
diagnosing malignant lymphoma Dogs=473
Total no herbicides Dogs=130=n2
19 were found to have lymphoma.
To Find:
a)What’s the standard error of the difference in the two proportions?
b) Construct a 95% confidence interval for this difference.
c) State an appropriate conclusion
Solution:
The standard error of difference is given by ,
Consider S1 for case 1 (herbicides) and S2 for case 2 (no herbicides)
So
[tex]S1-S2=Sqrt[p1(1-p1)/n1 +p2(1-P2)/n2)][/tex]
Here[tex]p1=473/827[/tex] =0.578 and [tex]p2=19/130[/tex]=0.146
[tex]S1-S2=Sqrt[0.572(0.428)/827 +0.146(0.854)/130][/tex]
[tex]S1-S2=Sqrt[2.96e-4 +9.59e-4][/tex]
[tex]S1-S2=Sqrt[0.001255][/tex]
[tex]S1-S2=0.0354[/tex]
This gives the difference between two proportions 0.0354
Now,
For 95 % C.I it is given by for above difference at Z=1.96
[tex]C.I.=[p1-p2-Z*Sqrt[p1(1-p1)/n1 +p2(1-P2)/n2) ,p1-p2+Z*Sqrt[p1(1-p1)/n1 +p2(1-P2)/n2)][/tex]
[tex]C.I=0.426-1.96*Sqrt[0.57(0.42)/827 +0.146(0.85)/130],0.426+1.96*Sqrt[0.57(0.42)/827 +0.146(0.85)/130][/tex]
[tex]C.I.=(0.356,0.495)[/tex]
The conclusion is that proportion of herbicides and no herbicides and having them diagnosed with malignant lymphoma is between 35.6 % and 49.5 % And higher than the proportion to pets in homes where no pesticides were used.
What are the x-intercepts of the following problem?
f(x) = (x - 2)(- 3)
7 critics liked the sequel to My Giant. This represents 10% of all critics. How many
critics reviewed it in all?
Answer: 70 critics
Step-by-step explanation: if 7 critics is 10% of all critics, and if 7 x 10 is 70, then there where 70 critics in total
70 critics reviewed the sequel of My Giant.
The number of critics who reviewed the sequel to My Giant can be calculated using the information given.
7 critics represent 10% of all critics. Let's denote the total number of critics as 'x'.
10% of x = 7 critics.
0.10x = 7
Solving for x, x = 70.
sally invests 10,500 in an account that earns 6% annual simple interest. assuming she makes no additional deposits or withdraws, how much interest will sally earn after 4 years?
Answer:
The interest is: $2520.00
Step-by-step explanation:
P is the principal amount, $10500.00.
r is the interest rate, 6% per year, or in decimal form, 6/100=0.06.
t is the time involved, 4....year(s) time periods.
So, t is 4....year time periods.
To find the simple interest, we multiply 10500 × 0.06 × 4 to get that
How many solutions does the graph of x2 + 100 = 0 have?
Answer:
there are two solutions
Step-by-step explanation:
x=10
x=-10
how many numbers have an absolute value of 6
Answer:
2
Step-by-step explanation:
Final answer:
The numbers that have an absolute value of 6 are -6 and 6.
Explanation:
An absolute value represents the distance between a number and zero on a number line. It is always a positive value. In this case, we are looking for numbers with an absolute value of 6. To find these numbers, we need to find all numbers that are 6 units away from zero.
The numbers that have an absolute value of 6 are: -6 and 6. These two numbers are equidistant from zero, with a distance of 6 units in either direction.
So, there are two numbers with an absolute value of 6.
The lemgth of a rectangle is 4 more than 2 times its width. Find the lemgth and width of the rectangle with an area of 160. What is the length and width?
Answer:
The length of the rectangle = 20
The width of the rectangle = 8
Step-by-step explanation:
Step(l):-
let 'W' be the width of the rectangle
Given the length of a rectangle is 4 more than 2 times its width
length of a rectangle(L) = 4+2W
Given the Area of rectangle = 160
Step(ii):-
we know that the area of the triangle = length ×width
(4+2w)w= 160
[tex]2w^{2} +4w-160=0[/tex]
[tex]2(w^{2} +2w- 80)=0[/tex]
[tex]w^{2} +10w-8w- 80=0[/tex]
[tex]w(w +10)-8(w+10)=0[/tex]
[tex](w+10)(w-8) =0[/tex]
[tex]w+10=0 , w-8=0[/tex]
w = -10 and w =8
Step(lll)
we can choose the width is 'w' = 8
now the length of the rectangle = 4+2(8) = 20
The width of the rectangle is '8'
Conclusion:-
The length of the rectangle = 20
The width of the rectangle = 8
Find the perimeter of the shape given length = x^2+4 and the width = 3x-4.Explain how you found your answer to problem .
Answer:
[tex]2x^{2}+6x[/tex]
Step-by-step explanation:
Perimeter is the distance all round a figure. Given length and width only, then this shale is likely to be a triangle. For a triangle, the area is given by
P=2(l+w)
Where l is the length and w is width.
Substituting w with 3x-4 and l with [tex]x^{2}+4[/tex]
then
[tex]P=2( x^{2}+4 +3x-4)=2( x^{2}+3x)=2x^{2}+6x[/tex]
Therefore, perimeter is [tex]2x^{2}+6x[/tex]
Which equation could be used to find the length of the hypotenuse?
Triangle A B C. Side A C is 2 feet and side C B is 5 feet. Hypotenuse A B is labeled c.
2 squared + 5 squared = c squared
2 squared + c squared = 5 squared
c squared minus 2 squared = 5 squared
5 squared minus 2 squared = c squared
Answer:
Step-by-step explanation:
leg1² + leg2² = hypotenuse²
AC² + BC² = AB²
2² + 5² = c²
Answer:
2² + 5² = c²
Step-by-step explanation:
2² + 5² = c²
:3
During an endurance race, part of a car's total distance traveled can be found by multiplying its top
speed (150 km/h) by the number of hours that it takes for the car to finish the race. The other part of
the total distance is the distance it takes for the car to get to top speed, in this case, % of a kilometer.
The car takes 0.01 hours to travel the initial % of a kilometer.
If the car reaches top speed, then drives at top speed for 3.75 hours, how far did the car travel during
the race?
1. Solve the problem above using simple arithmetic.
Answer:
563.25 km
Step-by-step explanation:
let [tex]d_1[/tex] be the the distance it takes for the car to get to top speed and [tex]d_2[/tex] be distance traveled can be found by multiplying its top speed (150 km/h) by the number of hours that it takes for the car to finish the race. The total distance d is given as:
[tex]d=d_1+d_2[/tex]
To get [tex]d_1[/tex], the car is initially at rest (i.e 0 km/h) and then it accelerates to a speed of 150 km/hr within 0.01 hrs. Let u = initial velocity = 0 km/hr, v = final velocity = 150 km/hr and the time taken ([tex]t_1[/tex]) = 0.01 hrs. Therefore:
[tex]d_1=(\frac{v+u}{2} )t=(\frac{0+150}{2} )0.01=0.75km[/tex]
To get [tex]d_2[/tex] , we use the formula [tex]d_2[/tex] = v[tex]t_2[/tex], where v =150 km / hr and [tex]t_2[/tex] = 3.75 hrs. Therefore:
[tex]d_2=150*3.75=562.5km[/tex]
[tex]d=d_1+d_2=562.5+0.75=563.25km[/tex]
What is the common denominator of 1/a + 1/b in the complex fraction 1/a-1/b divided by 1/a+ 1/b?
Answer:
common denominator of 1/a + 1/b is ab
however simplifying the complex fraction gives: (b-a)/(b +a)
Step-by-step explanation:
common denominator of 1/a + 1/b
should be the product of the denominators
a*b
so 1/a + 1/b = (b + a)/ab
ao
( 1/a - 1/b) divided by (1/a + 1/b) = (b - a)/(ab) divided by (b+a)/ab
To find the common denominator for 1/a and 1/b within a complex fraction, we use ab. The complex fraction (1/a - 1/b) divided by (1/a + 1/b) can be simplified by multiplying the numerator and denominator by ab, leading to a simplified form of (b² - a²) / (a² + b²).
When finding the common denominator for complex fractions like 1/a and 1/b, it's similar to dealing with real numbers. Given the complex fraction (1/a - 1/b) divided by (1/a + 1/b), we can identify a and b as the denominators. To combine the fractions within the complex fraction, we need a common denominator, which is ab. Thus, the fractions would become (b/a - a/b) and (a/b + b/a), both with a common denominator of ab.
In the complex fraction ((1/a - 1/b) / (1/a + 1/b)), by finding the common denominator, we then rewrite the equation as (b/a - a/b) / (a/b + b/a), which simplifies to (b² - a²) / (a² + b²) when multiplied by ab in both the numerator and the denominator. This process of finding the common denominator allows us to combine and simplify the complex fraction.
If a projectile is fired straight upward from the ground with an initial speed of 96 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2 + 96t. Find the maximum height of the projectile.
Answer:
144 feet
Step-by-step explanation:
The quadratic equation is:
[tex]h(t)=-16t^2+96t[/tex]
The general form of a quadratic is [tex]ax^2+bx+c[/tex]
So, we can match the equations and say:
a = -16
b = 96
c = 0
Now, for quadratic equations, the max value occurs at [tex]x=-\frac{b}{2a}[/tex] and the max value is what we get when we put that number in the function. First, lets find the value on which is occurs:
[tex]x=-\frac{b}{2a}\\x=-\frac{96}{2(-16)}\\x=3[/tex]
Now, put x = 3 into the equation:
[tex]h(t)=-16t^2+96t\\h(3)=-16(3)^2+96(3)\\h(3)=144[/tex]
The max height of projectile is 144 feet
1. Expand to write an equivalent expression: +(-8.+ 12y)
Answer:
-8 +12y
Step-by-step explanation:
a positive times a negative is negative so it stays the same
How can you rewrite log798 using the product
property?
Answer:
3 ways!
Step-by-step explanation:
-log72+log749 -log749= (2)-log798=2.356Answer:
log72+log749
log749=2
log798=2.356
Step-by-step explanation:
correct answers on edgn
Omar filled his gas tank for times last week. Here are the amounts of gas he bought 1.2,13.7,5.04,14. What is the total amount of gas omar bought last week
Answer: 33.94
Step-by-step explanation:
Last week, Omar filled his gas four times. The amounts of gas he bought are 1.2, 13.7, 5.04 and 14.
To get the total amount of gases bought by Omar, we add all the gases her bought the four times together. This gives:
1.2 + 13.7 + 5.04 + 14 = 33.94
This means that Omar bought a total gas of 33.94 last week.
Answer:
The total amount of gas Omar bought last week is 33.94
Step-by-step explanation:
Omar filled his gas four times and the amont of gas he bought are 1.2, 13.7, 5.04 and 14.
to estimate the total amount of gases Omar bought, we will sum up the amount of gas bought
1.2 + 13.7 + 5.04 + 14
= 33.94
Hence, the total amount of gas Omar bought last week is 33.94
Which must be true in order for the relationship ^zyx~^wvu to be correct
Answer:
Correct option: fourth one: ∠Z = ∠W and ∠X = ∠U
Step-by-step explanation:
There are 3 cases that gives similarity of two triangles:
Side-Angle-Side: They should have 2 sides and 1 angle in common
Side-Side-Side: They should have all 3 sides in commom
Angle-Angle: They should have 2 angles in common (therefore the third angle will also be equal)
In the first option, we have a pair of sides being parallel. That is not enough to prove similarity.
In the second option, two angles of the same triangle are equal, that's not enough, because the angles between each triangle can be different.
In the third option, two side of the same triangle are equal, that's not enough.
In the fourth option, two angles of the triangles are equal to each other, so this is the third case mencioned above, therefore it proves the similarity.
Correct option: fourth one.
Similar triangles may or may not be congruent.
The relationship that must be true for [tex]\mathbf{\triangle ZYZ \sim \triangle WVU}[/tex] is (d) [tex]\mathbf{\angle Z \cong \angle W }[/tex] and [tex]\mathbf{\angle X \cong \angle U }[/tex]
From the question, we understand that: [tex]\mathbf{\triangle ZYZ \sim \triangle WVU}[/tex]
The above means that, both triangles are similar (but not congruent). This means that:
The corresponding side lengths cannot be equalThe corresponding angles must be equalIn other words
[tex]\mathbf{\angle Z \cong \angle W }[/tex], [tex]\mathbf{\angle X \cong \angle U }[/tex] and [tex]\mathbf{\angle Y \cong \angle V }[/tex]
Hence, the true relationship is (d) [tex]\mathbf{\angle Z \cong \angle W }[/tex] and [tex]\mathbf{\angle X \cong \angle U }[/tex]
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URGENT: how many cubes with side lengths of 1/3 cm does it take to fill the prism
Answer:
48 cubes
Step-by-step explanation:
The total area of the cubes would be 1/27. Because 1/3*1/3*1/3=1/27.
The area of the prism is 16/9.
2 2/3 x 2/3=16/9
16/9 * 1 = 16/9
Because we want to find a common denominator we would multiply 16/9 by 3 to get 48/27.
Last, we take 48/27 and divide that by 1/27.
48/27 divided by 1/27 = 1296/27 = 48
Answer:
48 have a good day
Step-by-step explanation:
can u pls help i have a few mins left
i’m really confused someone help please
The radius of a circle is 8 miles. What is the length of a 90° arc?
Answer:
12.56 miles
Step-by-step explanation:
[tex]l = \frac{ \theta}{360 \degree} \times 2\pi \: r \\ \\ = \frac{ 90 \degree}{360 \degree} \times 2 \times 3.14 \times 8 \\ \\ = \frac{ 1}{4} \times 16 \times 3.14 \\ \\ = 4 \times 3.14 \\ = 12.56 \: miles[/tex]
Hence, length of arc = 12.56 miles
The weights of packages of crackers are normally distributed with a mean of 340 grams and a standard deviation of 12 grams.
What is the weight of a package of crackers with a z-score of −1.4 ?
Enter your answer in the box.
Answer: the weight of the package of crackers is 323.2 grams
Step-by-step explanation:
Since the weights of packages of crackers are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = weights of packages of crackers.
µ = mean weight
σ = standard deviation
From the information given,
µ = 340 grams
σ = 12 grams
The z score of the package is - 1.4
Therefore,
- 1.4 = (x - 340)/12
Cross multiplying by 12, it becomes
- 1.4 × 12 = x - 340
- 16.8 = x - 340
x = - 16.8 + 340
x = 323.2 grams
Problem 1
3x + y = –14
-2x-y=9
Answer:
x = -5 , y = 1
Step-by-step explanation:
Solve the following system:
{3 x + y = -14 | (equation 1)
-2 x - y = 9 | (equation 2)
Add 2/3 × (equation 1) to equation 2:
{3 x + y = -14 | (equation 1)
0 x - y/3 = (-1)/3 | (equation 2)
Multiply equation 2 by -3:
{3 x + y = -14 | (equation 1)
0 x+y = 1 | (equation 2)
Subtract equation 2 from equation 1:
{3 x+0 y = -15 | (equation 1)
0 x+y = 1 | (equation 2)
Divide equation 1 by 3:
{x+0 y = -5 | (equation 1)
0 x+y = 1 | (equation 2)
Collect results:
Answer: {x = -5 , y = 1
Marshall's office had already recycled 2 kilograms this year before starting the new recycling plan, and the new plan will have the office recycling 4 kilograms of paper each week. Write an equation that shows the relationship between the weeks w and the paper recycled p.
Write your answer as an equation with p first, followed by an equals sign.
Answer: w x 4 + 2 = p
Step-by-step explanation:
W = Week
P = Paper
4 kg a week would be 4 x w
you also must add the 2 kilograms at the start of the year
Eric is twice as tall as his little brother Kevin. Kevin is also three feet shorter than Eric. If we let E=Eric's height and let K= Kevin's height, translate these two sentences into 2 equations.
Answer:
The 2 equations are E = 2K and K = E-3
Step-by-step explanation:
Let the height of Eric be E
Let the height of Kevin be K
Eric is twice as tall as his little brother Kevin
E = 2K
Kevin is also three feet shorter than Eric
K = E-3
The 2 equations are E = 2K and K = E-3
Final answer:
Eric's height (E) is twice Kevin's height (K), represented by the equation E = 2K. Kevin is three feet shorter than Eric, which gives us the second equation K = E - 3. These equations help us determine their exact heights when solved together.
Explanation:
To translate the given information about Eric and Kevin's heights into two equations, we need to use the given relationship between their heights. From the statement 'Eric is twice as tall as his little brother Kevin,' we can write the first equation as E = 2K. This equation shows that Eric's height (E) is twice Kevin's height (K). The second statement 'Kevin is also three feet shorter than Eric' gives us the equation K = E - 3, which represents that Kevin's height is three feet less than Eric's height.
Together, these two equations can be used to solve for the exact heights of Eric and Kevin.
What is the volume of the following rectangular prism?
Answer:
33 units
Step-by-step explanation:
volume =area of base x height
volume = 9x (3 2/3)
volume= 33
According to given question, The volume of the rectangular prism is 72 cubic units.
The volume of a rectangular prism can be calculated by multiplying the length, width, and height of the prism. Let's say the length of the prism is 6 units, the width is 4 units, and the height is 3 units.
To find the volume, we use the formula: V = length × width × height. Substituting the given values, we get: V = 6 units × 4 units × 3 units. Multiplying the values, we find: V = 72 cubic units. Therefore, the volume of the rectangular prism is 72 cubic units.
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any one have the rest of the Surface Area and Volume Unit Test ??? please !!
Answer:
Second option is the right choice.
Step-by-step explanation:
[tex]Volume=2\pi rh+2\pi r^2\\\\V=2\left(3.14\right)\left(13\right)\left(14\right)+2\left(3.14\right)\left(13\right)^2\\\\\approx2205\:in^2[/tex]
A wheel with a diameter of 25 in. is in a puddle of water 8.1 in. deep. What is the width of the wheel, AB, at the surface of the water?
Please actually answer the question <3
Answer:
The length AB is 23.4in
Step-by-step explanation:
N/B please see the attached detailed diagram for your reference and better understanding
This problem bothers on the mensuration of flat shapes.
The width AB is the chord of the wheel
The radius of the whee r= 25/2= 12.5in
The depth of the wheel in the puddle is 8.1in
Let b be the distance from the surface AB to the diameter
b= 12.5-8.1 = 4.4in
Applying the formula
Chord Length = 2 *√(r²-b²)
=2*√(12.5²-4.4²)
= 2*√(156.25-19.36)
=2*√(136.89
=2*11.7
=23.4in
Kayla says that the point labeled C in the diagram below is the center, Raymond says that point C is the radius.
Who is correct and why?
Kayla is correct; the center is a fixed point in the middle of the sphere.
Kayla is correct; the center is a line segment from the center to the surface of the sphere.
Raymond is correct, the radius is the fixed point in the middle of the sphere.
Raymond is correct; the radius is a chord that is from the center to the surface of the sphere.
Answer:
The answers D
Step-by-step explanation:
Answer:
its: A
Step-by-step explanation:
The point which is the center or the middle point is located at the middle of the circle.
Jack’s mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
Answer:
16 friends
Step-by-step explanation:
If the question you're asking is how many friends he gave chocolates to, the answer would be 16.
50 - 2 = 48 (You subtract 2 because it's the amount of chocolates he had left)
48 ÷ 3 = 16 (Now you divide 48 by the number of chocolates he was giving his
friends. The final answer is the amount of times he gave out
chocolates, a.k.a how many friends he has