350 grams of magic steel and 350 grams of dragon alloy #33 is needed to make 700 grams of Dragon alloy #18.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of magic steel and y represent the amount of alloy #33, hence:
(0 * x) + (y * 0.28) = 700(1 - 0.86) (1)
Also:
x + (1 - 0.28)y = 0.86(700) (2)
From both equations:
x = 350, y = 350
350 grams of magic steel and 350 grams of dragon alloy #33 is needed to make 700 grams of Dragon alloy #18.
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Mark and paula are storing masks. Paula has 70% of the total number of masks. If paula has 840 more masks thatn mark, how many masks should paula give to mark si they both have an equal number of masks
Answer:
1050 masks per person.
Step-by-step explanation:
1) Create an equation to find the total number of masks
2) Solve equation and divide total by 2 to get the number of masks that can be given to both Mark and Paula so that they have equal number.
1) Since Paula has 70% of the total masks, it can be represented as 0.7 * t where t is the variable representing the total number of masks. Mark on the other hand has the remaining number of masks out of 100% which is 30%. We can express that as 0.3. We multiply that by t because he has 30% of the masks. The final equation we have is 0.3t + 840 = 0.7t. 840 because Paula has 840 more masks than Mark.
2) Solve by subtracting 0.3t from both sides leaving you with 0.4t = 840. We divide both sides by 0.4 to get 2100. That is the total number of masks. If we divide that number by 2, we get 1050.
A ladder is 8 feet 2 inches tall. How tall is it in inches?
Answer:
The ladder is 98 inches tall in inches.
Step-by-step explanation:
1 foot = 12 inches.⇒ 8 (feet) × 12 (inches) = 96 inches
⇒ Add the extra 2 inches
⇒ 98 inches tall.
The non-parallel sides of a trapezoid are called the
Answer:
Step-by-step explanation:
the legs
Explain how to graph the given piecewise-defined
function. Be sure to specify the type of endpoint each
piece of the function will have and why.
f(x)
X + 3, x < 2
3,
2 ≤ x < 4
4 - 2x,
X 2 4
The Piecewise -Defined function and how it is graphed is given below..
What is the explanation of how the Piecewise -Defined function is graphed?
Given the function in the attached image,
The Graph of f(x) = -x + 3 is drawn for x less than 2 because x is bounded.The Graph of f(x) = 3 is draw for x greater than and equal to 2 and less than 4 because x is bounded.The Graph of f(x) = 4 - 2x is draw for x greater than equal to 4 because x is bounded.See the attached Graph for better understanding.
f(x) = -x + 3 is coded purple.f(x) = 3 is coded orange.f(x) = 4 - 2x is coded green.Learn more about Piecewise -Defined function:
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According to Jaxs pedometer, he walked 2.783 km while taking care of the livestock in the morning and 3.124 km taking care of the livestock in the evening.
How far did Jax walk while taking care of the livestock today?
Answer:
5.907 km
Step-by-step explanation:
2.783 km + 3.124 km = 5.907 km
A customer's stock value seems to be rising exponentially. The equation for
the linearized regression line that models this situation is log(y) = 0.30x +0.296,
where × represents number of weeks. Which of the following is the best
approximation of the number of weeks that will pass before the value of the
stock reaches $600?
Considering the given regression equation, the number of weeks that will pass before the value of the stock reaches $600 is of:
B. 8.3.
What is the regression equation?The value of the stock y after x weeks is given as follows:
log(y) = 0.3x + 0.296.
We have to solve for x when y = 600, hence:
log(600) = 0.3x + 0.296
0.3x = 2.7782 - 0.296
x = (2.7782 - 0.296)/0.3
x = 8.3 weeks.
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(x-1)^2 + (y-2)^2 = 6.25
Answer: The center of the circle will be (1,2) and the radius will be 2.5
Step-by-step explanation: Basically since its (x-1) it would become x=1 so that's ur first value same thign with y but that would be ur second value. And since in your equation it is 6.25 that would be 2.5 because 6.25 is r^2 and you are looking for r.
Hellp please i need this super fast please
The surface area of the cone is 282.6 square centimeters.
How to get the surface area?
For a cone of radius R and height H, the surface area is given by:
[tex]A = pi*R^2 + pi*R*\sqrt{R^2 + H^2}[/tex]
Where pi = 3.14
In this case, we have:
R = 10cm/2 = 5cmH = 12 cm[tex]A = 3.14*(5cm)^2 + 3.14*5cm*\sqrt{(5cm)^2 + (12cm)^2} = 282.6 cm^2[/tex]
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Find the critical value (t-value) that form the boundaries of the critical region for a two-tailed test with a = 0.05 for a sample size of n1 =11 & n2 =8
Using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df is of Tc = 2.1098.
How to find the critical value of the t-distribution?It is found using a calculator, with two inputs, which are given by:
The confidence level.The number of degrees of freedom, which is one less than the sample size.In this problem, the inputs are given as follows:
Confidence level of 95%, as 1 - 0.05 = 0.95.17 degrees of freedom, as there are two samples, one with 11 - 1 = 10 df, and the other with 8 - 1 = 7 df, hence the total df is 10 + 7 = 17.Hence, using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df, using the stated two-tailed test, is of Tc = 2.1098.
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Please answer the question below . Help is greatly appreciated!
Using proportions, it is found that 40 ml of water have to be added to make the ratio of oil to water of 1:3.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The jar contains 100 ml of oil and water in the ratio 1:4, hence:
The amount of oil is: 1/5 x 100 = 20 ml.The amount of water is: 4/5 x 100 = 80 ml.Oil was added to make the ratio 1/2, hence:
[tex]\frac{20 + x}{100 + x} = \frac{1}[3}[/tex]
3(20 + x) = 100 + x
60 + 3x = 100 + x
x = 20.
Then there are 40 ml of oil and 80 ml of water, for a total of 120 ml. Now we want a ratio of 1:3, that is, 3/4 of the mixture being water, hence:
[tex]\frac{80 + x}{120 + x} = \frac{3}{4}[/tex]
4(80 + x) = 3(120 + x)
320 + 4x = 360 + 3x
x = 40
40 ml of water have to be added to make the ratio of oil to water of 1:3.
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19. Solve each equation by graphing. Round to the nearest tenth.
6x² +18x=0
3,6
0, -3
-3, -6
-1,6
Math 2
Answer:
0, -3
Step-by-step explanation:
Attachment.
In short, it is way easier to not graph it, however, if you really need to graph it, change it to the correct form, then do some plug and chug if the equation is not so friendly.
On Sunday, a local hamburger shop sold a combined total of 320 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Sunday?
Answer:
80
Step-by-step explanation:
1) if the number of hamburgers is 'h', number of cheesburgers is 'c', then
2) the condition 'The number of cheeseburgers sold was three times the number of hamburgers' can be written as c=3h. Also
3) the condition 'combined total of 320' can be written as h+c=320, then
4) it is possible to make up the system of equations:
[tex]\left \{ {{c=3h} \atop {c+h=320}} \right. \ = > \ \left \{ {{c=240} \atop {h=80}} \right.[/tex]
5) finally, number of hamburgers is 80.
what does 21/10 divided by 2 4/5 represent in this situation
Shayla enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. The area of the enlarged photo is 256 square inches. In the equation (x+10)^2=256, x represents the side measure of the original square photo. What are the dimensions of the original photo
. sorry sorrysorrysorrysorrysorrysorrysorrysorrysorrysorrysorry
Evaluate function expressions
Answer:
24
Step-by-step explanation:
1) according to the additional (see the attached picture) f(6)= -6 and g(5)= -5. Then
2) the given experssion can be written:
f(6)-6*g(5)=-6-6*(-5)=-6+30=24.
Suppose we want to choose 2 colors, without replacement from 3 colors red blue and green how many ways can this be done in the order of the choice is relevant and not relevant
The two colors can be chosen in 3 different ways.
In how many ways can we choose two colors?
If we have a set of N elements, the number of different sets of K elements (such that the order of the K elements does not matter) is:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
In this case, we have 3 colors, so N=3, and we want to choose 2, then K=2.
Replacing that we get:
[tex]C(3, 2) = \frac{3!}{(3- 2)!*2!} = \frac{3*2*1}{1*2*1} = 3[/tex]
The two colors can be chosen in 3 different ways.
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Simplify: Simplify: StartRoot StartFraction 27 x Superscript 12 Baseline Over 300 x Superscript 8 Baseline EndFraction EndRoot
The solution of the given expression is 9*[tex]x^{4}[/tex]/100.
GIven an expression equal to 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].
We have to simplify the expression in which variable comes only once.
Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.
The given fraction is 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].
When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.
=27[tex]x^{4}[/tex]/300
Now divide numerator an denominator by 3.
=9[tex]x^{4}[/tex]/300
Hence the expression 27[tex]x^{12} /300x^{8}[/tex] will look like [tex]9x^{4} /100[/tex] after simplifying.
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Answer:
[tex]Simplify:\sqrt\frac{27x^{12} }{300x^{8} }[/tex]
[tex]O \frac{9}{100}x^{4}[/tex]
✔ [tex]\frac{3}{10} x^{2}[/tex]
[tex]O \frac{27}{300} x^{4}[/tex]
[tex]O\frac{9}{10} x^{2}[/tex]
Consider the following functions. f=[(-1,1),(1,-2),(3,-4) and g=[(5,0),(-3,4),(1,1),(-4,1)} Find (f-g)(1) =
The difference between the functions give:
(f - g)(1) = f(1) - g(1) = -3
How to find the difference between the functions?
For two functions f(x) and g(x), the difference is defined as:
(f - g)(x) = f(x) - g(x).
Then:
(f - g)(1) = f(1) - g(1)
By looking at the given tables, we know that:
f(1) = -2
g(1) = 1
Replacing that we get:
(f - g)(1) = f(1) - g(1) = -2 - 1 = -3
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Between permanent life insurance and term life insurance, which typically has the lower premium and why?
a.
Term life insurance has the lower premium because term life insurance pays the face value to your beneficiary if you die within a certain set period of time, whereas whole life insurance covers you your entire life.
b.
Term life insurance has the lower premium because you cannot renew the insurance after your term has ended.
c.
Permanent life insurance has the lower premium because you are making more premium payments (your whole life versus a set period of time), so the amount per premium payment is less.
d.
Permanent life insurance has the lower premium because the amount you contribute is then invested and makes interest for the life insurance company.
Please select the best answer from the choices provided
A
B
C
D
Term life insurance has the lower premium because term life insurance pays the face value to your beneficiary if you die within a certain set period of time, whereas whole life insurance covers you your entire life. (Option A)
What is insurance?Insurance is when a third-party (the insurer) promises to indemnify another party (the insured) for losses they might suffer in the future in exchange for agreed upon payments.
Permanent life insurance is a type of insurance that provides a coverage that never expires. The person with a permanent life insurance is covered until he or she passes on. Whole life insurance is a type of permanent life insurance that has a fixed and guaranteed premium and a fixed death benefit.
Term life insurance is a type of insurance that provides coverage to a person only for a scheduled period of time. For example, a person who buys a 10 year term life insurance, the person's insurance only lasts for 10 years. If the person passes on within the 10 years, his beneficiary receives payments. If the person passes on after 10 years, his beneficiary does not receive any payments.
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A sample of 40 observations is selected from one population with a population standard deviation of 5. The sample mean is 102. A sample of 50 observations is selected from a second population with a population standard deviation of 6. The sample mean is 99. Conduct the following test of hypothesis using the .04 significance level.
Is this a one-tailed or a two-tailed test?
State the decision rule.
Compute the value of the test statistic.
What is your decision regarding H0?
What is the p-value?
1) This is a Two tailed Test.
2) Decision rule is; If the p-value is greater than 4% fail to reject H₀.
3) P-value = 0.00968764 and so we reject H₀
How to state the decision rule in hypothesis testing?We are given the hypothesis as;
Null Hypothesis; H₀: m₁ = m₂
Alternative Hypothesis; H₁: m₁ ≠ m₂
1) Since the alternative hypothesis has "not equal to sign", then it is a two tailed test.
2) Since we are told to use significance level as 0.04, then we can say that the decision rule is;
If the p-value is greater than 4% fail to reject H₀.
3) Using a 2-Sample Z-Test online TI calculator gives the test statistic as;
z = 2.5868
4) From z-score calculator, p-value equals 0.00968764. This is less than 0.04 and as such the decision regarding H₀ is to reject H₀.
5) P-value = 0.00968764
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What common base can be used to rewrite each side of the equation 2^x+3-3=5
The common base that can be used to rewrite each side of the equation is 2.
How to find the common base used to rewrite each equation?The common base that can be used to rewrite each side of the equation is as follows:
2ˣ⁺³ - 3 = 5
add 3 to both sides
2ˣ⁺³ - 3 + 3 = 5 + 3
2ˣ⁺³ = 8
Hence,
2ˣ⁺³ = 2³
Therefore, the common base that can be used to rewrite each side of the equation is 2.
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Find two sets of parametric equations for the rectangular equation. y=(x-6)^2-7x.
If x=t+6 then y=
If x=7t then y=
Show all work !
The two sets of parametric equations for the rectangular equation are;
If x=t+6 then y= t²-7t-42.If x=7t then y= 49t² - 133t +36.What are the parametric equations from the rectangular equation?It follows from the task content that the parametric equations can be determined as follows;
By substituting the x= t+6 into the rectangular equation; we have;
y = (t+6-6)²-7(t+6)
y = t²-7t-42.
By substituting the x= 7t into the rectangular equation; we have;
y = (7t-6)² -7(7t)
y = 49t² - 84t +36 - 49t
y = 49t² - 133t +36.
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Kaitlin,Scott and bill served a total of 81 orders on Monday .Kaitlin served 9 fewest orders than Scott .bill served 3 times as many orders as Scott . How many orders did they each serve?
Answer: Scott - 18, Kaitlin - 9, Bill - 54
Step-by-step explanation:
Let's view this as units. There are a total of 81 units. If we solve for Scott's orders:
Kaitlin served 9 fewer orders than Scott. We add 9 to 81 --> 9 + 81 = 90.
Now if we view Scott's orders as one unit:
Scott - 1 unit
Kaitlin (after adding 9) - 1 unit
Bill - 3 units (he served 3 times as many orders as Scott)
In total there are 3 + 1 + 1 = 5 units.
90 / 5 = 18.
Therefore, Scott served 18 orders.
18 - 9 = 9.
Kaitlin served 9 orders.
18 x 3 = 54.
Bill served 54 orders.
And to check our answer, 54 + 18 + 9 is 81.
How many words can be formed by using all the letters of the word AWILLO, if the two L's are to be separated?
For every 6,000 batches of 100 cards that are printed, she examines every 100th batch to make sure the logo is aligned and the magnetic strip works. Identify the population and the sample. a. population: 6,000 batches of 1000 cards sample: every 10,000 cards c. population: 6,000 batches of 1000 cards sample: every 100th batch b. population: 6,000 batches of 100 cards sample: every 10,000 cards. d. population: 6,000 batches of 100 cards sample: every 100th batch
Using sampling concepts, the population and the sample are given as follows:
d. population: 6,000 batches of 100 cards sample: every 100th batch.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and then:
The population is: All New York State residents.The sample is the 1000 randomly selected New York state residents.Hence, in the situation described the population is the 6,000 batches of 100 cards, while the sample is every 100th batch, hence option d is correct.
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Complete the frequency table:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.
The percentage of students age 15 and above travel to school by bus is 47%
How to complete the table?The table of values is given as:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
Using the column total of column 1, we have:
Under age 15 + 65 = 152
This gives
Under age 15 = 87
Using the column total of column 2, we have:
Age 15 and above + 18 = 110
This gives
Age 15 and above = 92
Using the row total of row 1, we have:
Car + 87 + 18 = 165
This gives
Car = 60
Using the row total of row 2, we have:
Car + 65 + 92 = 195
This gives
Car = 38
So, the complete frequency table is
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 87 18 60 165
Age 15 and above 65 92 38 195
Column totals 152 110 98 360
The percentage of students age 15 and above travel to school by bus is:
Percentage = 92/195 * 100%
This gives
Percentage = 47%
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what two numbers add to the number 30
Answer:
15+15
Step-by-step explanation:
Two 15's added together can equal 30
A yoga studio charges a $120 yearly fee for membership plus $16 for each class.
What is the average total cost per class if a studio member takes 100 classes per year?
Answer:
$17.2
Step-by-step explanation:
120 + 16*100 = 120 + 1600 = 1720
The member pays $1720 annually for 100 classes and membership fee combined.
1720/100 = 17.2
The student pays $17.2 per class on average.
9 cos(sin¯¹(x)) = √81 – 81x²
The equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S
To answer the question, we need to know what an equation is
What is an equation?An equation is a mathematical expression that show the relationship between two variables.
Given 9cos(sin¯¹(x)) = √(81 – 81x²), we need to show L.H.S = R.H.S
So, L.H.S = 9cos(sin¯¹(x))
= 9[√{1 - sin²(sin¯¹(x)}] (Since sin²y + cos²y = 1 ⇒ cosy = √[1 - sin²y])
9[√{1 - sin²(sin¯¹(x)}] = √9² × √{1 - sin²(sin¯¹(x)}]
= √[9² × {1 - sin²(sin¯¹(x)}]
= √[81 × {1 - sin²(sin¯¹(x)}]
= √[81 × {1 - x²}] (since sin²(sin¯¹(x) = [sin(sin¯¹(x)]² = x²)
= √(81 – 81x²)
= R.H.S
So, the equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S
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The Chief Operating Officer (COO) of the City Hotel has three people reporting to him: The Hotel Manager, The Retreat Coordinator and the Program Manager. The Hotel Manager has responsibility for the Front Desk, Housekeeping, Maintenance and Security. The Program Manager has responsibility for the Massage Therapists, the Yoga Instructors and the Dance Instructors. Draw a tree diagram representing these reporting relationships.
The tree diagram representing these reporting relationships is attached.
What is a tree diagram?It should be noted that a tree diagram is a planning tool that is used to show the hierarchy of tasks that are needed to be completed.
In this case, the tree diagram shows the way the employees report to each other.
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