Answer:
15 cartons of Hammers were ordered
Step-by-step explanation:
Cost per carton of Hammer = $100
Cost per carton of Wrenches = $150
Total Carton = 25
Total Cost = $3,000
Required
Determine the numbers of Hammer and Wrenches
Represent the hammers with H and the wrenches with W
So;
[tex]H + W = 25[/tex]
and
[tex]100H + 150W = 3000[/tex]
Make W the subject of formula in the first equation:
[tex]H + W = 25[/tex]
[tex]W = 25 - H[/tex]
Substitute 25 - H for W in the second equation
[tex]100H + 150(25 - H) = 3000[/tex]
[tex]100H + 3750 - 150H = 3000[/tex]
Collect Like Terms
[tex]100H - 150H = 3000 - 3750[/tex]
[tex]-50H = -750[/tex]
Divide both sides by -50
[tex]\frac{-50H}{=50} = \frac{-750}{-50}[/tex]
[tex]H = \frac{-750}{-50}[/tex]
[tex]H = 15[/tex]
Hence, 15 cartons of Hammers were ordered
A subcommittee is randomly selected from a committee of eight men and seven women. What is the probability that all three people on the subcommittee are men
Answer:
The probability that all three people on the subcommittee are men
= 20%
Step-by-step explanation:
Number of members in the committee = 15
= 8 men + 7 women
The probability of selecting a man in the committee
= 8/15
= 53%
The probability of selecting three men from eight men
= 3/8
= 37.5%
The probability that all three people on the subcommittee are men
= probability of selecting a man multiplied by the probability of selecting three men from eight men
= 53% x 37.5%
= 19.875%
= 20% approx.
This is the same as:
The probability of selecting 3 men from the 15 member-committee
= 3/15
= 20%
Write your height in inches. Suppose it increases by 15%, what would your new height be? Now suppose your increased height decreases by 15% after the 15% increase; what is your new height?
Answer:
New height= 41.4 inches
Second new height= 36inches
Step-by-step explanation:
Height is assumed to be 36 inches
If it increases by 15%.
15%= 0.15
It's new height =( 36*0.15) +36
New height= 5.4+36
New height = 41.4 inches
This expression (36*0.15) is the expression of adding 15% to the height.
So if the 15% is taken away again , height= 41.4-(36*0.15)
Height= 41.4-5.4
Height= 36 inches
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
The complete question is;
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
(a) less than 10 minutes
(b) longer than 5 minutes
(c) between 8 and 15 minutes
Answer:
A) P (x < 10) = 0.6700
B) P (x > 5 ) = 0.9406
C) P (8.0000 < x < 15.0000) = 0.6332
Step-by-step explanation:
A) we are given;
Mean;μ = 8.9 minutes
Standard deviation;σ = 2.5 minutes
Normal random variable;x = 10
So to find;P(x < 10) we will use the Z-score formula;
z = (x - μ)/σ
z = (10 - 8.9)/2.5 = 0.44
From z-distribution table and Z-score calculator as attached, we have;
P (x < 10) = P (z < 0.44) = 0.6700
B) similarly;
z = (x - μ)/σ =
z = (5 - 8.9)/2.5
z = -1.56
From z-distribution table and Z-score calculator as attached, we have;
P (x > 5 ) = P (z > -1.56) = 0.9406
C)between 8 and 15 minutes
For 8 minutes;
z = (8 - 8.9)/2.5 = -0.36
For 15 minutes;
z = (15 - 8.9)/2.5 = 2.44
From z-distribution table and Z-score calculator as attached, we have;
P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332
In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $112 with a standard deviation of $16. Use a 0.05 level of significance and determine whether or not the average room price is significantly different from $108.50.
Which form of the hypotheses should be used to test whether or not the average room price is significantly different from $108.50?
H0:
a. mu is greater than or equal to $108.50
b. mu is greater than $108.50
c. mu is less than $108.50mu is less than or equal to $108.50
d. mu is equal to $108.50mu is not equal to $108.50
Ha:
a. mu is greater than or equal to $108.50
b. mu is greater than $108.50mu is less than $108.50
c. mu is less than or equal to $108.50
d. mu is equal to $108.50mu is not equal to $108.50
Answer:
H0 :
a. mu is greater than or equal to $108.50
Ha:
c. mu is less than or equal to $108.50
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence
In the given scenario the test is to identify whether the average room price significantly different from $108.50. We take null hypothesis as mu is greater or equal to $108.50.
Find the solution to the system of equations.
Answer:
x = - 4, y = 7
Step-by-step explanation:
Given the 2 equations
- 7x - 2y = 14 → (1)
6x + 6y = 18 → (2)
Multiplying (1) by 3 and adding to (2) will eliminate the y- term
- 21x - 6y = 42 → (3)
Add (2) and (3) term by term to eliminate y
- 15x = 60 ( divide both sides by 15 )
x = - 4
Substitute x = - 4 into either of the 2 equations and evaluate for y
Substituting into (2)
6(- 4) + 6y = 18
- 24 + 6y = 18 ( add 24 to both sides )
6y = 42 ( divide both sides by 6 )
y = 7
An article reported on the results of an experiment in which half of the individuals in a group of 66 postmenopausal overweight women were randomly assigned to a particular vegan diet, and the other half received a diet based on National Cholesterol Education Program guidelines. The sample mean decrease in body weight for those on the vegan diet was 6 kg, and the sample SD was 3.2, whereas for those on the control diet, the sample mean weight loss and standard deviation were 3.8 and 2.4, respectively. Does it appear the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg? Carry out an appropriate test of hypotheses at significance level .05 based on calculating a P-value.
Answer:
We conclude that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg.
Step-by-step explanation:
We are given that an article reported on the results of an experiment in which half of the individuals in a group of 66 postmenopausal overweight women were randomly assigned to a particular vegan diet, and the other half received a diet based on National Cholesterol Education Program guidelines.
The sample mean decrease in body weight for those on the vegan diet was 6 kg, and the sample SD was 3.2, whereas, for those on the control diet, the sample mean weight loss and standard deviation were 3.8 and 2.4, respectively.
Let = true average weight loss for the vegan diet.
[tex]\mu_2[/tex] = true average weight loss for the control diet.
So, Null Hypothesis, : 1 kg {means that the true average weight loss for the vegan diet exceeds that for the control diet by less than or equal to 1 kg}
Alternate Hypothesis, : > 1 kg {means that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg}
The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\barX_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, = sample mean weight loss for the vegan diet = 6 kg
= sample mean weight loss for the control diet = 3.8 kg
= sample standard deviation weight loss for the vegan diet = 3.2 kg
= sample standard deviation weight loss for the control diet = 2.4 kg
[tex]n_1[/tex] = sample of vegan diet women = 33
[tex]n_2[/tex] = sample of control diet women = 33
Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(33-1)\times 3.2^{2}+(33-1)\times 2.4^{2} }{33+33-2} }[/tex] = 2.83
So, the test statistics = [tex]\frac{(6-3.8)-(1)}{2.83 \times \sqrt{\frac{1}{33}+\frac{1}{33} } }[/tex] ~ [tex]t_6_4[/tex]
= 1.722
The value of t-test statistics is 1.722.
Also, the P-value of the test statistics is given by;
P-value = P([tex]t_6_4[/tex] > 1.722) = 0.0461 or 4.61%
Since the P-value of our test statistics is less than the level of significance as 0.0461 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg.
Find the sum of the first six terms in the sequence (1,5,9,13....)
Answer:
The sum is 66
Step-by-step explanation:
There are a couple formulas to remember.
aₙ = a₁ + d(n-1)
Sₙ = [tex]\frac{n}{2}[/tex] · (a₁ + aₙ)
In your case "d" equals 4 and a₁ equals 1, that's how we know what the sequence will progress.
Let's plug in the values for the first equation:
aₙ = 1 + 4 (n-1)
Next we can simplify:
aₙ = 1 + 4n-4
aₙ = 4n - 3
Now we can plug in the value for "n" which is 6 for this particular problem:
a₆ = 4 · 6 - 3
a₆ = 21
We can now use the second equation to find the sum:
S₆ = [tex]\frac{6}{2}[/tex] · (1 + 21)
S₆ = 66
Hope this helps =)
[URGENT] (25 points) Ryan randomly drew a marble out of a bag of marbles, then put it back. He did
this 25 times. Of the 25 times he drew a red marble 6 times. He concluded
that the probability of drawing a red marble was
6/25
Answer:
Unpredictable
Step-by-step explanation:
Cuz if u look at it it is also random and u cant predict a random thing, so its quite simply unpredictable
Please answer this correctly without making mistakes I want expert genius or ace people to answer this correctly
Answer:
45.5 km
Step-by-step explanation:
18.3 km + 27.2 km = 45.5 km or 45 km and 500 m
Answer:
45.5km
Step-by-step explanation:
The distance between the locksmith and the furniture=18.3km
The distance between the furniture and the hotel=27.2km
S(locksmith)+S(furniture)=S(hotel)
18.3km+27.2km=45.5km
Hope this helps ;) ❤❤❤
Let me know if there is an error in my answer.
Strontium 90 is a radioactive material that decays according to the function Upper A (t )equals Upper A 0 e Superscript negative 0.0244 t Baseline commaA(t)=A0e−0.0244t, where Upper A 0A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 500500 grams of strontium 90. (a) What is the decay rate of strontium 90?
Answer:
Decay rate K = -2.44%
Step-by-step explanation:
From the question, we want to know the decay rate of strontium 90
Mathematically, this is accessible from its decay equation
From the decay equation, we can see that that ;
At = Ao e^-0.0244t
Generally, the decay equation of a radioactive sample can be written as
At = Ao e^-kt
where K represents the decay constant
From the equation, we can see that;
k = 0.0244 which when represented as a percentage is 2.44%
Since it’s a decay we can say that the decay rate is -2.44%
The answer is : -2.44%
what's the answer for this?
Answer:
6.4 miles
Step-by-step explanation:
Use pythogoras theorem here:
? ²= 5² + 4² =
?² = 25 + 16=
?²= 41
?= √41
? = 6.4
You don't need to thank me, I hope this helped
Answer:
Let d represent the distance from home to school
To find d we use the formula for Pythagoras theorem
That's
a² = b² + c²
Where a is the hypotenuse or the longest side
From the question
d is the hypotenuse
So we have
d² = 4² + 5²
d² = 16 + 25
d² = 41
d = √41 miles or 6.403 milesHope this helps you
A biology professor claimed that the proportions of grades in his classes are the same. A sample of 100 students showed the following frequencies:
Grade A B C D E
Frequency 18 20 28 23 11
Compute the value of the test statistics. Do the data provide enough evidence to support the professor’s claim?
Answer:
clearly the value of the test statistics shows that there are no enough evidence to support the claim that the proportion of the grads are the same.
Step-by-step explanation:
lets prove the statement by counter example, where if we have found the statement to be false for one then we conclude that it is false for all.
first lets explain what proportion is all about; proportion can be explained as the numerical relationship that compares things together.
in particular lets take grade A proportional to grade B which implies that 18:20
clearly if we observe here grade A is not same proportion with grade B. hence we conclude that there are no enough evidence to support the professor's claim.
Please! help and tell me the answers, or help me figure out these answers for 20 points? please! And please help me. Can anybody help me?
Answer:
1. Pattern (rule) : y = x-6
2. Pattern (rule) : y=x^2+1
3. Pattern (rule) : y = -3x
4. Pattern (rule) : y = 2x-2
5. Pattern (rule) : y = x^2
Step-by-step explanation:
Note: question number correspond to your order of questions.
1. Pattern (rule) : y = x-6
for missing parts, see attached table.
2. Pattern (rule) : y=x^2+1
3. Pattern (rule) : y = -3x
4. Pattern (rule) : y = 2x-2
5. Pattern (rule) : y = x^2
i would like some help thank you :)
Answer:
[tex]\angle AE = 32^{\circ}[/tex]
[tex]\angle EAD = 212^{\circ}[/tex]
[tex]\angle BE = 133^{\circ}[/tex]
[tex]\angle BCE = 227^{\circ}[/tex]
[tex]\angle AED = 180^{\circ}[/tex]
[tex]\angle BD = 79^{\circ}[/tex]
Step-by-step explanation:
The central angle of a circle is equal to 360º, whose formula in this case is:
[tex]\angle AB + \angle BC + \angle CD + \angle DE + \angle EA = 360^{\circ}[/tex]
In addition, the following conditions are known from figure:
[tex]\angle BC = 47^{\circ}[/tex], [tex]\angle DE = 148^{\circ}[/tex]
[tex]\angle DE + \angle EA = 180^{\circ}[/tex]
[tex]\angle CD + \angle DE = 180^{\circ}[/tex]
[tex]\angle AB + \angle BC + \angle CD = 180^{\circ}[/tex]
Now, the system of equations is now solved:
[tex]\angle EA = 180^{\circ}-\angle DE[/tex]
[tex]\angle EA = 180^{\circ}-148^{\circ}[/tex]
[tex]\angle EA = 32^{\circ}[/tex]
[tex]\angle CD = 180^{\circ}-\angle DE[/tex]
[tex]\angle CD = 180^{\circ}-148^{\circ}[/tex]
[tex]\angle CD = 32^{\circ}[/tex]
[tex]\angle AB = 180^{\circ} - \angle BC - \angle CD[/tex]
[tex]\angle AB = 180^{\circ}-47^{\circ}-32^{\circ}[/tex]
[tex]\angle AB = 101^{\circ}[/tex]
The answers are described herein:
[tex]\angle AE = 32^{\circ}[/tex]
[tex]\angle EAD = 212^{\circ}[/tex]
[tex]\angle BE = 133^{\circ}[/tex]
[tex]\angle BCE = 227^{\circ}[/tex]
[tex]\angle AED = 180^{\circ}[/tex]
[tex]\angle BD = 79^{\circ}[/tex]
What is the value of x plz help
Solve for one half on the triangle with height 6 and base would be 4/2 = 2
Use the Pythagorean theorem:
X = sqrt( 6^2 + 2^2)
X = sqrt( 36 + 4)
X = sqrt(40)
The answer is D
please help it's Factorisation with Numbers
Answer:
C.
6a + 18x + 18p
Step-by-step explanation:
3(2a + 6 (x + p)) firs multiply (x + p) with 6
3 (2a + 6x + 6z) now multiply inside the parenthesis with 3 and the answer would be 6a + 18x + 18p
The graphed line shown below is y = negative 4 x minus 12. On a coordinate plane, a line goes through (negative 3, 0) and (negative 2, negative 4). Which equation, when graphed with the given equation, will form a system that has no solution? y = 4 x + 12 y = negative 4 x y = negative 12 y = negative 4 (x + 3)
Answer:
y = -4x or the second option on edge.
This is because after you form it into the given equation, it equals y = -4x.
In order to clarify, edge also states that's the answer.
Answer:
2nd option
Step-by-step explanation:
One grade of tea costing $3.20 per pound is mixed with another grade costing $2.00 per pound to make 20
pounds of a blend that will sell for $2.72 per pound. How much of the $3.20 grade is needed? Formulate an
equation and then solve it to find how much of the $3.20 grade is needed.
Answer:
X+y = 20... equation 1
3.2x + 2y = 54.4...equation 2
X= 12
12 of $3.2 grade is needed
Step-by-step explanation:
Let x = grade containing$ 3.2 per pound
Let y = grade containing $2.00 per pound
X+y = 20... equation 1
X3.2 +2y = 20(2.72)
3.2x + 2y = 54.4...equation 2
Multiplying equation 1 by 2
2x +2y = 40
3.2x + 2y = 54.4
1.2x = 14.4
X= 12
If x= 12
2x +2y = 40
2(12) + 2y = 40
2y = 40-24
2y = 16
Y= 8
An integer is 7 more than 2 times another. If the product of the two integers is 60, then find the integers.
Answer:
15 and 4Step-by-step explanation:
Let the first integer be x and the second integer be y. If the first integer is 7 more than 2 times another, then x = 7+2y
The two integers will be y and 7+2y. If the product of both integers is 60, then;
y(7+2y) = 60
7y + 2y² = 60
2y² + 7y -60 = 0
2y²-8y+15y-60 = 0
2y(y-4)+15(y-4) = 0
(2y+15)(y-4) = 0
2y+15= 0 and y-4 = 0
2y = -15 and y = 4
y = -15/2 and 4
Taking the positive integer, y = 4
To get the other integer, we will substitute y = 4 into the equation x = 7+2y;
x = 7+2(4)
x = 7+8
x = 15
Hence the two integrs are 15 and 4
Identify the type of hypothesis test below. H0:X=10.2, Ha:X>10.2 Select the correct answer below: The hypothesis test is two-tailed. The hypothesis test is left-tailed. The hypothesis test is right-tailed.
Answer:
The hypothesis test is right-tailed
Step-by-step explanation:
To identify a one tailed test, the claim in the case study tests for the either of the two options of greater or less than the mean value in the null hypothesis.
While for a two tailed test, the claim always test for both options: greater and less than the mean value.
Thus given this: H0:X=10.2, Ha:X>10.2, there is only the option of > in the alternative claim thus it is a one tailed hypothesis test and right tailed.
A test with the greater than option is right tailed while that with the less than option is left tailed.
Answer:
Please help with questions on my profile somebody
Step-by-step explanation:
We want to estimate the population mean within 5, with a 99% level of confidence. The population standard deviation is estimated to be 15. How large a sample is required? (Round up your answer to the next whole number.)
Answer: 60
Step-by-step explanation:
Formula to calculate sample size (n):
[tex]n=(\dfrac{\sigma\times z^*}{E})^2[/tex]
, where [tex]\sigma[/tex] = population standard deviation, E Margin of error , z* = critical value for the confidence interval.
As per given , we have
E =5
[tex]\sigma=15[/tex]
Critical value for 99% confidence = 2.576
Then,
[tex]n=(\dfrac{15\times2.576}{5})^2\\\\\Rightarrow\ n=59.721984\approx60[/tex]
So, Required sample size = 60 .
23 increased by twice Janelle's savings Use the variable j to represent Janelle's savings.
Answer:
2x+23
Step-by-step explanation:
A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the life spans of the tires have a bell-shaped distribution.
(a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000 miles. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual.
(b) The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span.
Answer:
Step-by-step explanation:
From the information given:
mean life span of a brand of automobile = 35,000
standard deviation of a brand of automobile = 2250 miles.
the z-score that corresponds to each life span are as follows.
the standard z- score formula is:
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]
For x = 34000
[tex]z = \dfrac{34000 - 35000}{2250}[/tex]
[tex]z = \dfrac{-1000}{2250}[/tex]
z = −0.4444
For x = 37000
[tex]z = \dfrac{37000 - 35000}{2250}[/tex]
[tex]z = \dfrac{2000}{2250}[/tex]
z = 0.8889
For x = 3000
[tex]z = \dfrac{30000 - 35000}{2250}[/tex]
[tex]z = \dfrac{-5000}{2250}[/tex]
z = -2.222
From the above z- score that corresponds to their life span; it is glaring that the tire with the life span 30,000 miles has an unusually short life span.
For x = 30,500
[tex]z = \dfrac{30500 - 35000}{2250}[/tex]
[tex]z = \dfrac{-4500}{2250}[/tex]
z = -2
P(z) = P(-2)
Using excel function (=NORMDIST -2)
P(z) = 0.022750132
P(z) = 2.28th percentile
For x = 37250
[tex]z = \dfrac{37250 - 35000}{2250}[/tex]
[tex]z = \dfrac{2250}{2250}[/tex]
z = 1
Using excel function (=NORMDIST 1)
P(z) = 0.841344746
P(z) = 84.14th percentile
For x = 35000
[tex]z = \dfrac{35000- 35000}{2250}[/tex]
[tex]z = \dfrac{0}{2250}[/tex]
z = 0
Using excel function (=NORMDIST 0)
P(z) = 0.5
P(z) = 50th percentile
a. The z score of each life span should be -0.4444, 0.889, and 2.2222.
b. The percentile of each life span should be 0.0228, 0.8413 and 0.5000.
Given that,
mean life span of 35,000 miles, with a standard deviation of 2250 miles.The calculation is as follows:(a)
The z score should be
[tex]Z1 = \frac{34000-35000}{2250} = -0.4444\\\\Z2 = \frac{37000-35000}{2250} = 0.8889\\\\Z3 = \frac{30000-35000}{2250} = -2.2222\\\\[/tex]
The tire with life span of 30000 miles would be considered unusual
(b)
The percentile should be
[tex]Z1 = \frac{30500-35000}{2250} = -2[/tex]
p(Z1 < -2) = NORMSDIST(-2) = 0.0228
[tex]Z2 = \frac{37250-35000}{2250} = 1[/tex]
p(Z2 < 1) = NORMSDIST(1) = 0.8413
[tex]Z3 = \frac{35000-35000}{2250} = 0[/tex]
p(Z3 < 0) = NORMSDIST(0) = 0.5000
Find out more information about standard deviation here:
https://brainly.com/question/12402189?referrer=searchResults
the solution of the equation 0=4+4(m+1) is
Answer:
[tex]\boxed{m = -2}[/tex]
Step-by-step explanation:
[tex]0 = 4+4(m+1)[/tex]
Resolving Parenthesis
[tex]0 = 4+4m + 4[/tex]
[tex]0 = 4m+8[/tex]
Subtracting 8 to both sides
[tex]-8 = 4m[/tex]
[tex]4m = -8[/tex]
Dividing both sides by 4
m = -8/4
m = -2
Step-by-step explanation:
4+4m+4= 0
4m+8=0
4m=-8
m= -8/4=-2
Explain how to write an equivalent expression using the
associative property.
2+(11 + y)
Answer:
2+(11+y)=(2+11)+y=11+(2+y)
Answer:
Sample Response: The associative property allows you to keep the order of the terms and change the position of the parentheses. So you can rewrite the terms in the same order and then move the parentheses so that the 2 + 11 is now inside. The equivalent expression is (2 + 11) + y.
Step-by-step explanation:
E d g e n u i t y
Can anyone help? I am stuck. Find m∠G.
Answer:
80
Step-by-step explanation:
The quadrilateral is a kite.
The angle opposite to angle H is equal to angle H.
Angle F = 110 degrees
Angles in a quadrilateral add up to 360 degrees.
60 + 110 + 110 + G = 360
280 + G = 360
G = 360 - 280
G = 80
The measure of angle G is 80 degrees.
Answer: 80 degrees.
Step-by-step explanation:
In a kite, the angles formed by noncongruent sides are congruent. Thus, <EFG is 110 degrees. Then, because a kite is a quadrilateral, all of the angles in it add up to 360. Thus, is <FGH = x, then 110+110+60+x=360. Thus, x = 80.
Hope it helps <3
Solve for y: 3(2y + 4) = 4(2y – 1/2).
The solution is y =
Answer:
Answer y=7
Step-by-step explanation:
find the maximal area of a right triangle with hypotenuse of length 8
Answer:
Max area is 16
Step-by-step explanation:
If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.
So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.
The maximal area of a right triangle is 90.496
What is differentiation?Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given:
let the perpendicular be 'x'
and base be 'y'
Using Pythagoras theorem
x² + y² = 8²
x² + y² = 64
y²= 64- x²
y = √64-x²
Now, Area of triangle
= 1/2* base* height
=xy/2
=x *√64-x²*1/2
On differentiating both side
A' = 64-2x²/√64-x²*1/2
Setting derivative function equal to zero,
64= 2x²
32=x²
x=5.656
So, Area of triangle = x *√64-x²*1/2
= 90.496
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Fake Question: Should Ujalakhan01 be a moderator? (If you could answer I'd appreciate it haha.)
Real Question: Simplify [tex](a^5*a^4)+(b^2*b^3)-(c^7*c^6)[/tex]
Answer:
[tex]a^9 + b^ 5 + c^{13}[/tex]
Step-by-step explanation:
[tex](a^5 \times a^4)+(b^2 \times b^3) + (c^7 \times c^6)[/tex]
When bases are same and it is multiplication, then add the exponents.
[tex](a^{5+4})+(b^{2+3})+(c^{7+6})[/tex]
[tex](a^9)+(b^ 5) + (c^{13})[/tex]
Apply rule : [tex](a^b)=a^b[/tex]
[tex]a^9 + b^ 5 + c^{13}[/tex]
Answer:
[tex]a^9+b^5-c^{13[/tex]
Step-by-step explanation:
[tex](a^5*a^4) + (b^2*b^3)-(c^7*c^6)[/tex]
When bases are same, powers are to be added.
=> [tex](a^{5+4})+(b^{2+3})-(c^{7+6})[/tex]
=> [tex]a^9+b^5-c^{13[/tex]
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15:115:115, colon, 1. He currently has 404040 grams of the spice blend, and he can go buy more if necessary. He wants to make 101010 servings, where each serving has 757575 grams of rice. Overall, David spends 4.504.504, point, 50 dollars on rice.
Answer:
.006
:)
Step-by-step explanation:
8 servings can David make with the current amount of spice.
What is Ratio?Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
The rice-to-spice ratio = 15:1
The 75 grams of rice in one serving will require
⇒75/15
⇒5 gram of spice.
David's inventory of 40 gram of spice is enough for
40 g/(5 g/serving) = 8 servings
Hence, 8 servings can David make with the current amount of spice.
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