Answer:
The individually paid $1.5 for the tip and $8.5 for the food
Step-by-step explanation:
Total money spent = $40
Food bill = $34
if the situation is represented by the equation [tex]\frac{1}{4}(t+34) = \frac{40}{4}[/tex] where t is the amount of the tip, the amount for the tip can be calculated as shown;
[tex]\frac{1}{4}(t+34) = \frac{40}{4}\\ t+34 = 40\\t = 40-34\\t = 6[/tex]
Amount of the tip = $6
If they decided to split the bill and tip evenly among themselves, amount paid by each friend for the food and the tip can be gotten using the equation representing the situation where t = $6 as shown;
[tex]= \frac{1}{4}(t+34) \\= \frac{1}{4}(6+34)\\= \frac{1}{4}(6)+\frac{1}{4}(34)\\= 1.5+8.5\\[/tex]
From the result above, it can be seen that each friend paid $1.5 for their tip and $8.5 for their food
Answer:
A) Each friend paid $8.50 for the food and $1.50 for the tip.
Katie is making hair clips to sell at the craft fair. To make each hair clip, she uses 1 barrette and 1 precut ribbon. The barrettes are sold in packs of 12, and the precut ribbons are sold in packs of 9. How many packs of each item does she need to buy to make the least number of hair clips with no supplies left over?
Answer:
3 packs of barrettes and 4 packs of ribbons.
Step-by-step explanation:
All we need to do here is to find the least common multiple between 12 and 9.
We can factor both of these numbers to do so.
12: 3*4: 3*2*2
9: 3*3
We can cancel out one 3 (since it appears in both prime factorizations) and multiply what we have left to find the LCM.
2*2*3*3=36
This means that she will be making 36 clips/needs 36 of each item.
36/12=3
3 packs of barretes.
36/9=4
4 packs of ribbons.
What is the length of Line segment B C?
11
23
40
60
Answer:
40
Step-by-step explanation:
An isosceles triangle is a triangle that has 2 congruent/equal sides and 2 congruent angles.
Side AB and side BC are the same length (the red tick marks shows that the sides are congruent)
Since they are the same length, you can set them equal to each other
Side AB = Side BC
x + 17 = 2x - 6 Subtract x on both sides
17 = x - 6 Add 6 on both sides
23 = x
Now that you know "x", you can find the length of Side BC:
2x - 6 Plug in 23 for "x"
2(23) - 6
46 - 6 = 40
Answer:
Yes, the answer is C! (40)
A sample of a radioactive substance has an initial mass of 58.7 . This substance follows a continuous exponential decay model and has a half-life of 5 hours. (a)Let t be the time (in hours) since the start of the experiment, and let y be the amount of the substance at time t . Write a formula relating y to t. y=__ e^__(t) . Use exact expressions to fill in the missing parts of the formula. Do not use approximations. b)How much will be present in 8 hours? Do not round any intermediate computations, and round your answer to the nearest tenth.
Answer:
a). Y = y0e^-k(t)
b) Y = 19.4 Unit mass
Step-by-step explanation:
Y = y0e^-k(t)
Where y is amount present at the time
Y0 is initial amount present at t = 0
Y0 = 58.7
Half life = 5 hours
At half life , y = 58.7/2
At half life , y = 29.35
K = decaying constant.
Let's look fithe value of k
Y = y0e^-k(t)
29.35 = 58.7e^-k(5)
29.35/58.7 = e^-k(5)
0.5 = e^-k(5)
In 0.5 = -k(5)
-0.69314718 = -k(5)
0.138629436 = k
The value present in 8 hours will be
Y = y0e^-k(t)
Y = 58.7e-0.138629436(8)
Y = 58.7e-1.109035488
Y = 58.7(0.329876978)
Y= 19.36377861
To the nearest tenth
Y = 19.4 unit of mass
An object is dropped from the top of a tower with a height of 1160 feet. Neglecting air resistance, the height of the object at time t seconds is given by the
polynomial - 16t square + 1160. Find the height of the object at t = 1 second.
The height of the object at 1 second is feet.
Answer:
Height at t = 1 sec is 1144 ft
Step-by-step explanation:
Given:
Initial height of object = 1160 feet
Height of object after t seconds is given by the polynomial:
[tex]- 16t ^2+ 1160[/tex]
Let [tex]h(t)=- 16t ^2+ 1160[/tex]
Let us analyze the given equation once.
[tex]t^2[/tex] will always be positive.
and coefficient of [tex]t^2[/tex] is [tex]-16[/tex] i.e. negative value.
It means something is subtracted from 1160 ft (i.e. the initial height).
So, height will keep on decreasing with increasing value of t.
Also, given that the object is dropped from the top of a tower.
To find:
Height of object at t = 1 sec.
OR
[tex]h (1)[/tex] = ?
Solution:
Let us put t = 1 in the given equation: [tex]h(t)=- 16t ^2+ 1160[/tex]
[tex]h(1)=- 16\times 1 ^2+ 1160\\\Rightarrow h(1) = -16 + 1160\\\Rightarrow h(1) = 1144\ ft[/tex]
So, height of object at t = 1 sec is 1144 ft.
ga political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate only wants a 8% margin of error at a 95% cnofidence level, what size of sample is needed
Answer: 151
Step-by-step explanation:
if prior population proportion is unknown , then the formula is used to find the sample size :
[tex]n=0.25(\frac{z_{\alpha/2}}{E})^2[/tex]
, where [tex]z_{\alpha/2}[/tex] = Two tailed critical value for significance level of [tex]\alpha.[/tex]
E = Margin of error.
Given : margin of error = 8%= .08
For 95% confidence level , two tailed critical value = 1.96
Now, the required sample size :
[tex]n=0.25(\frac{1.96}{0.08})^2\\\\=0.25(24.5)^2\\\\=150.0625\approx151[/tex]
Hence, the size of the sample needed = 151.
Write an equation that is 10 less than 3 times a number y, multiplied by 2 and divided by 4. (10 less than 3 times a number y is to be done first)
Answer: (3y - 10)*2÷4
Step-by-step explanation:
Because 10 less than 3 times a number, y, is done first, it is in parenthesis. The 3 is there to represent the "three times" and the -10 is there to represent the "ten less". The *2 is there to represent the "multiplied by two" and the ÷4 is there to represent the "divided by 4"
Hope it helps, and tyvm <3
Answer:
[tex]\displaystyle \frac{2(3y - 10)}{4}[/tex]
Step-by-step explanation:
10 less than 3 times y.
The variable y is multiplied by 3, 10 is subtracted from 3 × y.
The result 3y - 10 is then multiplied by 2.
2(3y - 10) is then divided by 4.
What ray is a common side of
how many sixths are in 4
how many two-thirds are in 2
Answer:
24 sixths in 4 and 3 two-thirds
Step-by-step explanation:
6=24 sixths in 4
Answer:
24 sixth's are in 4 and 3 two-third's are in 2
Step-by-step explanation:
4 ÷ 1/6 = 4 * 6 = 24
2 ÷ 2/3 = 2 * 3/2 = 3
What is the sqr root of x times the sqr root of x?
Answer:
Just x
Step-by-step explanation:
√x times √x equals √x²
√x² = x
How many different words can be formed with the letters AAAABBCCD (not necessarily meaningful words)?
Please help me with this. Other answers did not work.
Answer:
the answer is 9! ÷ (4! * 2! * 2!)
Step-by-step explanation:
The different words that can be formed with the letters AAAABBCCD will be 3780.
What is permutation?
The permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters.
We have,
AAAABBCCD
i.e.
Total number of letters = 9
Letter A repeated = 4 times
Letter B repeated = 2 times
Letter C repeated = 2 times
Now,
Using the permutation formula,
Permutation (ⁿPr) = n! / r!
So,
Number of ways = 9! / [ 4! × 2! × 2!] = [9 × 8 × 7 × 6 × 5 × 4!] / [ 4! × 2! × 2!] = 3780
Hence we can say that the different words that can be formed with the letters AAAABBCCD will be 3780.
To learn more about Permutation click here,
https://brainly.com/question/1216161
#SPJ2
find the value of x...
Answer:
x = 7
Step-by-step explanation:
This problem can be solved using angular bisector theorem.
It states that if any angle of triangle is bisected by a line , then that line
divides the opposite side of that angle in same proportion as that of two other sides which contain the angle.
__________________________________
Here one angle is is divided into parts theta
Thus,
using angular bisector theorem
14/21 = 6/3x-12
=> 14(3x-12) = 21*6
=> 3x-12 = 21*6/14 = 9
=> 3x = 12+9 = 21
=> x = 21/3 = 7
Thus, x = 7
Sam invests $6000 in two different accounts. The first account paid 12 %, the second account paid 7 % in interest. At the end of the first year he had earned $590 in interest. How much was in each account? $_____ at 12% $_____ at 7%
Answer:
The amount in the account at 12% interest is $3400 and the amount in the second account at 7% interest is $2600
Step-by-step explanation:
Let x be the amount in the account at 12% interest
So, 6000-x is the amount in the second account at 7% interest
[tex]SI = \frac{P \times T \times R}{100}[/tex]
First account:[tex]SI=\frac{x \times 1 \times 12}{100}[/tex]
Second account : [tex]SI =\frac{(6000-x) \times 1 \times 7}{100}[/tex]
We are given that At the end of the first year he had earned $590 in interest.
So, [tex]\frac{x \times 1 \times 12}{100}+\frac{(6000-x) \times 1 \times 7}{100}=590\\x=3400[/tex]
So,the amount in the account at 12% interest is $3400
The amount in the second account at 7% interest =6000-x=6000-3400=2600
Hence the amount in the account at 12% interest is $3400 and the amount in the second account at 7% interest is $2600
Suppose H is an ntimesn matrix. If the equation Hxequalsc is inconsistent for some c in set of real numbers R Superscript n, what can you say about the equation Hxequals0? Why?
Answer:
The answer is explained below
Step-by-step explanation:
Given that, the equation H*x = c is inconsistent for some c in R^n, we can say that the equation A*x = b has at least one solution for each b in R^n of IMT (Inverse Matrix Theorem) is not fulfilled.
Thanks to this we can say that by equivalence of theorem statement, the equation H*x = 0 will not have only the trivial solution. It will have non-trivial solutions too.
Match each phrase on the left with every correct temperature on the right. Some
answer choices on the right will not be used.
Freezing point of water
0°C
Boiling point of water
0°F.
32°F
100°C
212°F
100°F
I NEED HELP PLEASE, THANKS! :)
Answer:
Symmetric with respect to the polar axis in agreement with the second answer listed.
Step-by-step explanation:
This is the shape of a cardioid [tex]14\,(1+cos(\theta))[/tex] it contains the function cosine of the angle so it must be symmetric with respect to the polar axis, since the cosine function is also symmetric for positive and negative values of the angle.
Factor this trinomial.
х^2 - 9х+ 20
А. (х- 4)(х+ 5)
В. (х-2)(х+ 10)
С. (х-2)(х- 10)
D. (x-4)(х - 5)
Answer:
D
Step-by-step explanation:
We're looking for two numbers that have a sum of -9 and a product of 40. These 2 numbers are -4 and -5 so the answer is (x - 4)(x - 5).
Answer:
(x-4)(x-5)
Step-by-step explanation:
х^2 - 9х+ 20
What 2 numbers multiply to 20 and add to -9
-4*-5 = 20
-4+-5 = -9
(x-4)(x-5)
quanto e 500x6-51-5x50
Answer:
2699
Step-by-step explanation:
you do all the multiplication first
500×6= 3000
5 ×50 = 250
so it becomes
3000-51-250 = 2699
Answer:
2699
Step-by-step explanation:
Last winter Armand had StartFraction 5 Over 6 EndFraction of a row of stacked logs. At the end of the winter he had StartFraction 8 Over 15 EndFraction of the same row left. How much wood did he burn over the winter?
Answer:
3/10
Step-by-step explanation:
We have that the Armans last winter had 5/6 of a row of stacked logs and at the end of the winter he had 8/15 of the same row left, therefore:
Ambitious
First we have to do is that the denominator is the same.
in the case of 5/6 it would be 25/30
and for 8/15 it would be 16/30
Now if we can do the subtraction and it would be:
25/30 - 16/30 = 9/30 or what equals 3/10
3/10 was the amount of wood he burned in the winter
Answer:
D) 3/10 row
Step-by-step explanation:
Suppose you are told that the grades of the nal exam of your class follows a normal distribution. The average score is 65 and the variance is 12. What is the the probability of a random classmate getting a score more than 80?
Answer:
0% probability of a random classmate getting a score more than 80
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 65, \sigma = \sqrt{12} = 3.4641[/tex]
What is the the probability of a random classmate getting a score more than 80?
This is 1 subtracted by the pvalue of Z when X = 80. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 65}{3.4641}[/tex]
[tex]Z = 4.33[/tex]
[tex]Z = 4.33[/tex] has a pvalue of 1
1 - 1 = 0
0% probability of a random classmate getting a score more than 80
Find the median of: 1, 3, 4, 6, 2, 4, 5, 6, 2, 3, 1, 4, 0, 4, 4, 4, 8, 9, 7, 4
Answer:
4
Step-by-step explanation:
1, 3, 4, 6, 2, 4, 5, 6, 2, 3, 1, 4, 0, 4, 4, 4, 8, 9, 7, 4
Arrange the numbers from smallest to largest
0,1, 1,2,2, 3,3, 4, 4,4,4,4,4 , 4, 5, 6, 6, 7, 8, 9,
There are 20 numbers
The middle number is between 10 and 11
0,1, 1,2,2, 3,3, 4, 4,4 ,4,4,4 , 4, 5, 6, 6, 7, 8, 9,
The median is 4
Solution,
Arranging the data in ascending order:
0,1,1,2,2,3,3,4,4,4,4,4,4,4,5,6,6,7,8,9
N(total number of items)= 20
Now,
Median:
[tex] (\frac{n + 1}{2)} ) ^{th \: item} \\ = (\frac{20 + 1}{2} ) ^{th \: item} \\ = \frac{21}{2} \\ = 10.5 \: th \: \: item[/tex]
Again,
Median:
[tex] \frac{10 \: th \: item + 11 \: th \: item}{2} \\ = \frac{4 + 4}{2} \\ = \frac{8}{2} \\ = 4[/tex]
Two parallel lines are crossed by a transversal.What is the value of d?
Step-by-step explanation:
if there is any confusion then again ask me always with you
Answer:
d = 125
Step-by-step explanation:
E2020
pls mark Brainliest
Finding missing angles
Answer:
x=15
Step-by-step explanation:
165+x=180
180-165=15
Hope this helps!!
The number of hours worked per year per person in a state is normally distributed with a standard deviation of 39. A sample of 15 people is selected at random, and the number of hours worked per year per person is given below. Calculate the 98% confidence interval for the mean hours worked per year in this state. Round your answers to the nearest integer and use ascending order.Time205120612162216721692171218021832186219521962198220522102211
Answer:
[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]
[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]
And the confidence interval would be given by (2137, 2203)
Step-by-step explanation:
2051 ,2061 ,2162 ,2167 , 2169 ,2171 , 2180 , 2183 , 2186 , 2195 , 2196 , 2198 , 2205 , 2210 ,2211
We can calculate the mean and deviation with these formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
And we got:
[tex]\bar X=2169.67[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean
s=48.72 represent the sample standard deviation
n=15 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=15-1=14[/tex]
Since the Confidence is 0.98 or 98%, the significance is [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and using excel we calculate the critical value [tex]t_{\alpha/2}=2.624[/tex]
Now we have everything in order to replace into formula (1):
[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]
[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]
And the confidence interval would be given by (2137, 2203)
true or false? the circumcenter of a triangle is the center of the only circle that can be inscribed about it
Answer:
TRUE
Step-by-step explanation:
The circumcenter of a triangle is the center of the only circle that can be circumscribed about it
Answer:
False
Step-by-step explanation:
5. In the figure below, triangles CPW and
BHM are congruent. Which statement must be true?
Answer:
C. side CW ≅ side BM,
Step-by-step explanation:
When two triangles are said to be congruent, it means they have the same shape and size. This implies that their corresponding sides and corresponding angles are equal.
Therefore, given that triangles CPW and BHM are congruent, their corresponding sides should be equal.
Thus, the statement side CW ≅ side BM, must be true.
Other statements given are not true.
Find the value of x.
Answer:
[tex]\huge\boxed{x=\sqrt{66}}[/tex]
Step-by-step explanation:
ΔADC and ΔABD are similar (AAA)
Therefore the cooresponging sides are in proportion:
[tex]\dfrac{AD}{AC}=\dfrac{AB}{AD}[/tex]
Substitute
[tex]AD=x;\ AC=6+5=11;\ AB=6[/tex]
[tex]\dfrac{x}{11}=\dfrac{6}{x}[/tex] cross multiply
[tex](x)(x)=(11)(6)\\\\x^2=66\to x=\sqrt{66}[/tex]
Don’t know this one
Answer:
B
Step-by-step explanation:
The answer is B because in order for the square root of a number to be equal to another number, the answer squared should be the number under the square root.
B. [tex](-4)^2\neq -16[/tex].
Hope this helps.
Suppose you are starting your own company selling chocolate covered strawberries. You decide to sell the milk chocolate covered strawberries for a profit of $2.25 $ 2.25 /box and the white chocolate covered strawberries at $2.50 $ 2.50 /box. Market tests and available resources, however, have given you the following constraints. The combined production level should not exceed 800 800 boxes per month. The demand for the white chocolate is no more than half the demand for milk chocolate strawberries. The production level for white chocolate should be less than or equal to 200 200 boxes.
Answer:
$1850 per month
Step-by-step explanation
There are two types of chocolates that can be produced milk chocolate and strawberry covered chocolate. To find the profit we make following equation,
P = $2.25 SC + $2.50 WC
where SC is strawberry chocolate and WC is White milk chocolate.
The maximum production level can be 800 boxes per month and white chocolates can not exceed the 200 boxes per month so we assume making 600 boxes of Strawberry covered chocolates and 200 boxes of white chocolates.
Profit = 2.25 * 600 + 2.50 * 200
Profit = $1850
This is the maximum profit that can be earned after making combination of two types of chocolates.
There are no solutions to the system of inequalities shown below.
y< 3x+ 5
y> 3x-1
True or false
Someone help please
Answer:
False, there are actually infinite solutions as these are parallel lines.
Step-by-step explanation:
Please answer this correctly
Answer:
2/7
Step-by-step explanation:
The numbers greater than 7 or less than 3 are 2 and 8.
2 numbers out of 7.
P(greater than 7 or less than 3) = 2/7
Answer:
2/7
Step-by-step explanation:
There are a total of 7 sample spaces also known as 2,3,4,5,6,7,8. Now we have to find a number greater than 7 and less than 3. 2 is less than 3, and 8 is greater than 7, so two numbers are selected. This would become 2/7 because out of all of the 7 outcomes, only two are selected.