Answer:
1. (y - x)² = 256
2. 128g needed to be added
Step-by-step explanation:
1.
9 + 5 + 2 + y + x = 2(8 + 4 + 1 + 3 + x)
16 + y + x = 32 + 2x
y - x = 16
∴ (y - x)² = 256
2.
x = mass of alcohol to add
480 × 0.24 = 115.2 ← current mass of alcohol
0.4(480 + x) = 115.2 + x (×5)
2(480 + x) = 576 + 5x
960 + 2x = 576 + 5x
3x = 384
x = 128g
Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit. Select all that apply.
{f(x) = 2(3)^x
{g(x) = 10log(x+3)
(-1.9, 15.9)
(-2, 0.2)
(1.9, -15.9)
(2, -0.2) (1.9, 15.9)
Answer:
closest choice: (-2, 0.2)
Step-by-step explanation:
The attached image from a graphing calculator shows the solutions (to the nearest tenth) to be ...
(-1.9, 0.2)
(1.0, 6.0)
The closest of the offered choices is (-2, 0.2). None are actually correct.
Mrs. Fields needs more chocolate chips to make cookies. The store has bags that weigh 0.45 lbs., 0.434 lbs., and 0.4 lbs. Which bag should she purchase if she wants the most chocolate chips?
Answer:
bag weigh 0.45 lbs
Step-by-step explanation:
From a barrel of colored marbles, you randomly select 1 blue, 2 yellow, 7 red, 6 green, and 2 purple marbles. Find the experimental probability of randomly selecting a marble that is NOT yellow.
A: 8/9
B: 9/10
C: 11/18
D: 7/9
Answer:
8/9
Step-by-step explanation:
1 blue, 2 yellow, 7 red, 6 green, and 2 purple marbles = 18 marbles
The number that are not yellow = total - yellow
P( not yellow) = number that are not yellow / total
= (18-2) / 18
= 16/18
=8/9
A hot dog has about 1/4 the amount of protein as 3 ounces of hamburger. Together, they have about 25 grams of protein. How many grams of protein are in a 3 oz hamburger?
Answer:
(1) protein in hot dog = ¼ * protein in 3 ounces of hamburger
(2) protein in hot dog + protein in 3 ounces of hamburger = 25
So we need to re-arrange (1) and (2) to solve for the protein in 3 ounces of hamburger!
(re-arrange (1)): 4 * protein in hot dog = protein in 3 ounces of hamburger
(re-arrange (2)): protein in hot dog = 25 - protein in 3 ounces of hamburger
(plugging re-arranged (2) into re-arranged (1)):
4 * (25 - protein in 3 ounces of hamburger) = protein in 3 ounces of hamburger ( multiplying )
100- 4 protein in 3 ounces of hamburger = protein in 3 ounces of hamburger
solving for the protein in 3 ounces of hamburger:
5 * protein in 3 ounces of hamburger = 100
protein in 3 ounces of hamburger = 20 gram
Hypothetical Situation: A scientist notices that her bees may be avoiding a specific pollen from flower "X" despite its abundance in the area. To test to see if this behavior is reproducible and not anecdotal, she decides to provide a choice test to her bees. She does this by putting the bees in a small cage with two dishes. One with pollen from flower "X" the other is pollen from a flower that she knows her bees collect, flower "Y." She counts how many times the bees chooses Flower "X" vs Flower "Y" and collects this data.
What is experimental group?
Answer:
The experimental group in this case are the group of bees that are put in the small cage.
Step-by-step explanation:
The experimental group is the group of subjects that participate in the test. They are usually assigned to the treatments in study. In some cases there is a control group, with no assigned treatment.
In this case, the bees that she put in the cage, and they are not assigned to a particular treatment. It can be considered a control group.
Find five consecutive integers such that the sum of the first and 5 times the third is equal to 41 less than 3 times the sum of the second fourth and fifth
Answer:
see below
Step-by-step explanation:
We'll cal the first integer x and then the rest of them will be x + 1, x + 2, x + 3 and x + 4. We can write x + 5(x + 2) = 3(x + 1 + x + 3 + x + 4) - 41.
x + 5x + 10 = 3(3x + 8) - 41
6x + 10 = 9x + 24 - 41
6x + 10 = 9x - 17
3x = 27
x = 9
The numbers are 9, 10, 11, 12, 13.
Alice studies the relationship between climate and heart disease around the world. H(t)H(t)H, left parenthesis, t, right parenthesis models the probability for the occurrence of heart disease (in percents relative to the global average) at an area where the temperature is ttt degrees Celsius. According to Alice's model, when the temperature is -5\degree\text{ C}−5° Cminus, 5, degree, start text, space, C, end text (which is the lowest temperature included in the model), the probability is 10\%10%10, percent above average. Then the probability decreases until the temperature reaches 30\degree\text{ C}30° C30, degree, start text, space, C, end text (which is the highest temperature included in the model), where the probability is 20\%20%20, percent below average. Which number type is more appropriate for the domain of HHH?
Answer:
The domain of the function H(t), is [-5, 30].
The range of the function H(t), is [(10% + average), (average - 20%)]
Step-by-step explanation:
The domain of a function is the complete set of possible values of the independent variable.
For this question, the function is H(t), with the temperature, t, serving as the independent variables and H(t) the evidently dependent variable.
The domain of a function refers to all the possible independent variable values that will give corresponding real dependent variable values.
For this question, Alice's model has the probability for the occurrence of heart disease (in percents relative to the global average) at an area, H(t) varying with the temperature of that area in degree Celsius.
At a temperature of -5°C (the lowest temperature in the model), the probability is 10% above the average.
Then, the probability decreases with increase in temperature, taking a value 20% lower than the average when the temperature is at its highest of 30°C in the model.
So, temperature ranges from -5°C to 30°C and the probability for the occurrence of heart disease ranges from 10% above the average to 20% below the average.
The domain of the function H(t), from the definition given above would therefore be [-5, 30]
And the range of the function H(t), is [(10% + average), (average - 20%)]
Hope this Helps!!!
The Real Number type is more appropriate fro the domain of H(t).
The domain of H(t) is given as [tex]-5 \leq t \leq 30[/tex]
Given that:
The lowest temperature included in the model is -5° C
The highest temperature included in the model is 30° C
The domain of H includes the values of the temperature. Since the temperature can be non integer too, sometimes rational too, thus we use Real Number type for the domain of H(t).
The domain of H(t) will be given by the following interval on real number line:
[tex]\begin{aligned} Domain(H(t)) = [-5, 30]\\\end{aligned}[/tex]
or [tex]-5 \leq t \leq 30[/tex].
Hence, the Real Number type is more appropriate fro the domain of H(t).
The domain of H(t) is given as [tex]-5 \leq t \leq 30[/tex].
Learn more here:
https://brainly.com/question/9463453
The number of pieces of popcorn in a large movie theatre popcorn bucket is normally distributed, with a mean of 1610 and a standard deviation of 10. Approximately what percentage of buckets contain between 1600 and 1620 pieces of popcorn?
Answer:
A
Step-by-step explanation:
We know that in normal distribution, approximately 34% of bags will fall with in one standard deviation on one side. On both sides within the range of 1 standard deviation, 34 + 34 = 68 % of bags will fall.
Our range is:
1600 to 1620
1610 - 10 to 1610 + 10
So the answer is 1
That means, that 68% is the answer.
Answer:
The answer is A.
Step-by-step explanation:
Approximately 68%
A credit card had an APR of 15.98% all of last year, and compounded interest daily. What was the credit card's effective interest rate last year?
A.
17.32%
B.
17.20%
C.
16.96%
D.
16.62%
Answer:
Option(B) is the correct answer to the given question.
Step by Step Explanation
We know that
[tex]A\ =\ P \ *(\ 1+\ \frac{r}{n} \ ) ^{nt}[/tex]
Here A=amount
r=15.98%=0.1598
n=365
t=1
Putting these values into the equation
[tex]A\ =\ P \ *(\ 1+\ \frac{0.1598}{365} \ ) ^{365}[/tex]
[tex]A\ =\ P \ *(\ 1+\ 0.000437) ^\ { 365}[/tex]
[tex]A\ =\ P \ *(\ 1.000437 ) ^{365}[/tex]
[tex]A\ =1.17288 P[/tex]
Now we find the interest
I=[tex]1.17288P\ -P\\=\ 0.17288P\\\ ~ 0.1720P[/tex]
Therefore effective interest rate of the last year can be determined by
[tex]\frac{0.1720P}{P}[/tex]
=0.1720 *100
=17.20%
Answer:
17.32%
Step-by-step explanation:
The Employment and Training Administration reported that the U.S. mean unemployment
insurance benefit was $238 per week (The World Almanac, 2003). Aresearcher in the state
of Virginia anticipated that sample data would show evidence that the mean weekly unemployment
insurance benefit in Virginia was below the national average.
a. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s
contention.
b. For a sample of 100 individuals, the sample mean weekly unemployment insurance
benefit was $231 with a sample standard deviation of $80. What is the p-value?
c. At αα = .05, what is your conclusion?
d. Repeat the preceding hypothesis test using the critical value approach.
Answer:
Step-by-step explanation:
a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 238
For the alternative hypothesis,
H1: µ < 238
This is a left tailed test
b) Since the population standard deviation is not given, the distribution is a student's t.
Since n = 100
Degrees of freedom, df = n - 1 = 100 - 1 = 99
t = (x - µ)/(s/√n)
Where
x = sample mean = 231
µ = population mean = 238
s = samples standard deviation = 80
t = (231 - 238)/(80/√100) = - 0.88
We would determine the p value using the t test calculator. It becomes
p = 0.19
c) Since alpha, 0.05 < than the p value, 0.19, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed insignificant evidence that the mean weekly unemployment insurance benefit in Virginia was below the national average.
d) Since α = 0.05, the critical value is determined from the t distribution table. Recall that this is a left tailed test. Therefore, we would find the critical value corresponding to 1 - α and reject the null hypothesis if the test statistic is less than the negative of the table value.
1 - α = 1 - 0.05 = 0.95
The negative critical value is - 1.66
Since - 0.88 is greater than - 1.66, then we would fail to reject the null hypothesis.
Please help me with this question!!!
Answer:
3(cos(75°) +i·sin(75°)) and 3(cos(255°) +i·sin(255°))
Step-by-step explanation:
Using Euler's formula, this can be written as ...
x^2 = 9·e^(i5π/6)
Then the square roots are ...
x = (±√9)e^((i5π/6)/2) = ±3e^(i5π/12)
Of course, multiplying by -1 is the same as adding 180° to the angle.
The square roots are ...
3(cos(75°) +i·sin(75°)) and 3(cos(255°) +i·sin(255°))
if F (x) equals 4x + 7 which of the following is the inverse of F(x)
Answer:
[tex]F^{-1}(x)=\dfrac{x-7}{4}[/tex]
Step-by-step explanation:
To find the inverse function, solve for y the relation ...
F(y) = x
4y +7 = x
4y = x - 7
y = (x -7)/4 . . . . the inverse function
[tex]\boxed{F^{-1}(x)=\dfrac{x-7}{4}}[/tex]
what two numbers add to -7 and multiply to -60
Answer:
The answer would be 5 and -12
arl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute? 2 feet 12 feet 720 feet 7,200 feet
Answer: 720 ft
Step-by-step explanation: He rides 720 feet.
if 120 feet are in 10 seconds then;
60 seconds are 60/10*120=720 feet
Answer:
720
Step-by-step explanation:
120/10 to find his feet per second which is 12 feet per second
12*60
since there are 60 seconds in a minute
= 720
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 The test statistic to test the null hypothesis equals _____.
Answer:
The test statistic to test the null hypothesis equals 1.059
Step-by-step explanation:
From the given information; we have:
Treatment Observations
A 20 30 25 33
B 22 26 20 28
C 40 30 28 22
The objective is to find the test statistic to test the null hypothesis; in order to do that;we must first run through a series of some activities.
Let first compute the sum of the square;
Total sum of squares (TSS) = Treatment sum of squares [tex](T_r SS)[/tex] + Error sum of squares (ESS)
where:
(TSS) = [tex]\sum \limits ^v_{i=1} \sum \limits ^{n_i}_{j-1}(yij- \overline {y}oo)^2[/tex] with (n-1) df
[tex](T_r SS)[/tex] [tex]= \sum \limits ^v_{i=1} n_i( \overline yio- \overline {y}oo)^2[/tex] with (v-1) df
[tex](ESS) = \sum \limits ^v_{i=1} \sum \limits ^{n_i}_{j-1}(yij- \overline {y}io)^2[/tex] with (n-v) df
where;
v= 3
[tex]n_i=[/tex]4
i = 1,2,3
n =12
[tex]y_{ij}[/tex] is the [tex]j^{th[/tex] observation for the [tex]i^{th[/tex] treatment
[tex]\overline{y}io[/tex] is the mean of the [tex]i^{th[/tex] treatment i = 1,2,3 ; j = 1,2,3,4
[tex]\overline y oo[/tex] is the overall mean
From the given data
[tex]\overline y oo = \dfrac{1}{12} \sum \limits ^3_{i=1} \sum \limits ^{4}_{j=1}(yij)^2= 27[/tex]
[tex]TSS = \dfrac{1}{12} \sum \limits ^3_{i=1} \sum \limits ^{4}_{j=1}(yij- 27)^2 = 378[/tex]
[tex]T_r SS= \sum \limits^3_{i=1}4 (\overline y io - \overline yoo)^2[/tex]
[tex]=4(27-27)^2+4(24-27)^2+4(30-27)^2 = 72[/tex]
Total sum of squares (TSS) = Treatment sum of squares [tex](T_r SS)[/tex] + Error sum of squares (ESS)
(TSS) = 378 - 72
(TSS) = 306
Now; to the mean square between treatments (MSTR); we use the formula:
MSTR = TrSS/df(TrSS)
MSTR = 72/(3 - 1)
MSTR = 72/2
MSTR = 36
The mean square within treatments (MSE) is:
MSE = ESS/df(ESS)
MSE = 306/(12-3)
MSE = 306/(9)
MSE = 34
The test statistic to test the null hypothesis is :
[tex]T = \dfrac{ \dfrac{TrSS}{\sigma^2}/(v-1) }{ \dfrac{ESS}{\sigma^2}/(n-v) } = \dfrac{MSTR}{MSE} \ \ \ \approx \ \ T(\overline {v-1}, \overline {n-v})[/tex]
[tex]T = \dfrac{36}{34}[/tex]
T = 1.059
What is the volume of a rectangular prism with a length of 12ft, a width of 10ft, and a height of 18ft?
Answer:
2160ft³
Step-by-step explanation:
V=whl=10·18·12=2160ft³
in a survey of more than 3000 people 93% of the respondents claimed to prefer Isaac's immaculate ice cream over any other brand of ice cream. which of the folloling groups were surveyed.
Answer:
The answer is 2,790.
Step-by-step explanation:
Here's a handy tool.
93% of 1 = 0.93 93% of 131 = 121.83 93% of 261 = 242.73 93% of 391 = 363.63
93% of 2 = 1.86 93% of 132 = 122.76 93% of 262 = 243.66 93% of 392 = 364.56
93% of 3 = 2.79 93% of 133 = 123.69 93% of 263 = 244.59 93% of 393 = 365.49
93% of 4 = 3.72 93% of 134 = 124.62 93% of 264 = 245.52 93% of 394 = 366.42
93% of 5 = 4.65 93% of 135 = 125.55 93% of 265 = 246.45 93% of 395 = 367.35
93% of 6 = 5.58 93% of 136 = 126.48 93% of 266 = 247.38 93% of 396 = 368.28
93% of 7 = 6.51 93% of 137 = 127.41 93% of 267 = 248.31 93% of 397 = 369.21
93% of 8 = 7.44 93% of 138 = 128.34 93% of 268 = 249.24 93% of 398 = 370.14
93% of 9 = 8.37 93% of 139 = 129.27 93% of 269 = 250.17 93% of 399 = 371.07
93% of 10 = 9.30 93% of 140 = 130.20 93% of 270 = 251.10 93% of 400 = 372.00
If 4/3 * 3/4 = 5k, then k =
Answer:
1/5
Step-by-step explanation:
switch sides, delete both common factors and your stuck with 5k=1. then you put both in a fraction and it gets you 1/5
Can someone please help me
Answer:
6
Step-by-step explanation:
Similar triangles. MNE is ABC but 3/4 the size. Multiply each side by 3/4 to get lengths.
x = 8 *3/4 = 6
A survey taken in a large statistics class contained the question: "What's the fastest you have driven a car (in miles per hour)?" The five-number summary for the 87 males surveyed is: min = 55, Q1 = 95, Median = 110, Q3 = 120, Max = 155 Should the largest observation in this data set be classified as an outlier? No Yes
Answer:
NO
Step-by-step explanation:
To find out which observation to classify as an outlier, whether the largest or not, a very good approach or way to do this is to apply the 1.5(IQR) rule.
According to the rule, for finding the largest observation in the data that can be classified as an outlier, we would use the formula = Q3 + 1.5(IQR).
Q3 = 120
IQR = Q3 - Q1 = 120 - 95 = 25
Lets's plug these values into Q3 + 1.5(IQR)
We have,
120 + 1.5(25)
= 157.5
Since our max in the observation is given as 155, the largest observation in the data set cannot be set as an outlier because 157.5 which we got from our calculation is higher than the max value we have in the data set.
Our answer is NO.
However, the smallest observation should be set as outlier because:
Q1 - 1.5(IQR) = 95 - (1.5*25) = 57.5, which gives us an outlier that falls within our data range.
Jacob put his 731 Marbles and 37 bags if he puts the same amount in each bag how many marbles were in each bag how many marbles were left out of the backs
Answer:
19 marbles in each bag 28 left over
Step-by-step explanation:
the first step to this problem is to find out the number of marbles in each bag.
if there were 731 marbles and 37 bags, we need to divide 731 by 37.
731/37 = 19[tex]\frac{28}{37}[/tex]
therefore there are 19 marbles in each bag.
the second part of the question is to determine how many are left out or in other words how many numbers are "left over"
since the fraction is 28/37 there are 28 marbles that are left out of the bag.
feel free to ask questions, hope this helped you!
Write the quotient in simplest form. Type answer as integer or a fraction
Answer:
[tex]-\dfrac{1}{26}[/tex]
Step-by-step explanation:
[tex]-\dfrac{12}{13}\div 24=\\\\-\dfrac{12}{13} \times \dfrac{1}{24}=\\\\-\dfrac{12}{13\times 24}=\\\\-\dfrac{1}{26}[/tex]
Hope this helps!
Which of these levelers will make it easier to lift the object
Answer:
C
Step-by-step explanation:
Because it would have less weight to carry
Which cosine function has maximum of 0.5, a minimum of -0.5, and a period of 2(pi)/3
Answer:
The answer is "[tex]\bold{y=0.5 \cos 3 \theta}[/tex]"
Step-by-step explanation:
The choices were missing the question so the answer to this question can be defined as follows:
The answer is [tex]y= 0.5 \cos 3\theta[/tex] because:
[tex]\Rightarrow -1 \leq \cos 3 \theta \leq 1\\\\\Rightarrow -0.5 \leq \cos 3 \theta \leq 0.5\\[/tex]
So, the maximum value is = 0.5 and the minimum value is = -0.5 of [tex]\frac{2\pi}{3}[/tex].
Answer:
D. y= 0.5 cos 3 theta
Step-by-step explanation:
What is the value of x?
Answer:
x= 70
Step-by-step explanation:
These are supplementary angles
45+2x-5 = 180
Combine like terms
40+2x= 180
Subtract 40 from each side
40+2x-40 =180-40
2x= 140
Divide by 2
2x/2 =140/2
x = 70
In the first year if ownership, a new car lose 20% of its value. If a car lost $4,200 value in the first year, how much did the car originally cost?
Answer:
21,000$
Step-by-step explanation:
part to whole method
20/100 and 4,200/
How many 20s to get to 4,200?
Venera sent a chain letter to her friends, asking them to forward the letter to more friends.
The relationship between the elapsed time t, in months, since Venera sent the letter, and the number of
people, P(t), who receive the email is modeled by the following function:
3t+7
P(t) = 2
Complete the following sentence about the monthly rate of change in the number of people who receive
the email.
Round your answer to two decimal places.
Every month, the number of people who receive the email is multiplied by a factor of
Answer:
It is multiplied by a factor of 8
Step-by-step explanation:
Every month, the number of people who receive the email is multiplied by a factor of 8.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
Venera sent a chain letter to her friends, asking them to forward the letter to more friends.
The relationship between the elapsed time t, in months, since Venera sent the letter, and the number of people, P(t), who receive the email is modeled by the following function:
[tex]\rm P(t) = 2^{3t+7}[/tex]
Every month, the number of people who receive the email is multiplied by a factor will be
For t = 2, we have
P(2) = 2³⁽²⁾⁺⁷
P(2) = 2¹³
For t = 3, we have
P(3) = 2³⁽³⁾⁺⁷
P(3) = 2¹⁶
Then the factor will be
⇒ P(3) / P(2)
⇒ 2¹⁶ / 2¹³
⇒ 2³
⇒ 8
More about the exponent link is given below.
https://brainly.com/question/5497425
#SPJ2
Which expression is equivalent to log Subscript 8 Baseline 4 a (StartFraction b minus 4 Over c Superscript 4 Baseline EndFraction)?
Answer:
[tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex].
Step-by-step explanation:
The given expression is
[tex]\log_84a\left(\dfrac{b-4}{c^4}\right)[/tex]
Using the properties of logarithm, we get
[tex]\log_84+\log_8a+\log_8\left(\dfrac{b-4}{c^4}\right)[/tex] [tex][\because \log_a mn=\log_a m+\log_a n][/tex]
[tex]\log_84+\log_8a+\log_8(b-4)-\log_8c^4[/tex] [tex][\because \log_a \frac{m}{n}=\log_a m-\log_a n][/tex]
[tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex] [tex][\because \log_a x^n =n\log_a x][/tex]
Therefore, the required expression is [tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex].
Answer:
B on edge
Step-by-step explanation:
Assuming that a cheese sandwich consists of 2 slices of bread and 3 slices of cheese, determine the number of whole cheese sandwiches that can be prepared from 32 slices of bread and 51 slices of cheese. g
Answer:
Only 16 whole sandwiches can be produced
Step-by-step explanation:
From the question, we know that we will need two slices of bread to make a full sandwich.
We can divide the number of slices of bread by two to check how many full sandwiches can be made.
Number of complete sets of bread = 32/2 = 16 sets
Similarly, we can divide the number of slices of cheese by 3 to find out the number of complete sets of cheese that will be there:
Number of complete sets of cheese = 51/3 = 17 sets
Since we have more cheese than bread, the number of whole sandwiches that can be made will be limited to the number of sets of bread available. (in this case, the ingredient smaller in quantity will be used to limit the production) which is = 16
Therefore only 16 whole sandwiches can be produced
Jamie needs the following items from the hardware store a drill bit that cost 4.99 nails that caused 0.46 and sandpaper that cost 0.89 how much money was spent if the sales tax rate is 6%
Answer: $5.96
Step-by-step explanation:
4.99 + 0.46 + 0.89 is what she paid, not with tax. That equals 6.34.
Applying 6% means we calculate 6% of 6.34 and then subtract it from 6.34. (Or, we can also calculate 100-6%=94% of 6.34). Either way, the answer is 5.9596, or rounded, 5.96.
Hope that helped,
-sirswagger21
