Answer:
[tex] - 3(x + 4) {}^{2} - 4[/tex]
Step-by-step explanation:
Vertex form is
[tex]a(x - h) {}^{2} + k = f(x)[/tex]
We know that h and k are both -4. Let x be -2 and y be -16.
[tex]a( - 2 + 4) {}^{2} - 4 = - 16[/tex]
[tex]a(2) {}^{2} - 4 = - 16[/tex]
[tex]4a - 4 = - 16[/tex]
[tex]4a = - 12[/tex]
[tex]a = - 3[/tex]
So the equation in vertex form is
[tex] - 3(x + 4) {}^{2} - 4[/tex]
What is the conversion factor from meters to centimeters?
10,000 meters per centimeter
100 meters per centimeter
100 centimeters per meter
10,000 centimeters per meter
Answer: there are 100 centimeters in 1 meter. Meters to centimeters multiply by 100. Centimeters to meters divide by 100.
Step-by-step explanation:
Meters to centimeters multiply by 100
(10,000 m ) (100) = 1,000,000 cm.
(100 m) (100) = 10,000 cm.
Centimeters to meters divide by 100.
100 cm / 100 = 1 meter
10,000 cm /100 = 100 m
Find the smallest possible value of x+y so that x^2 − y^2 is divisible by 74, where x and y are positive integers.
Answer: 2
Step-by-step explanation:
We know by different of squares, (x-y)(x+y)=74. Since we need to find the smallest possible answer for x+y, we let x+y=2, where both x and y = 1.
Paul can install a 300-square-foot hardwood floor in 18 hours. Matt can install the same floor in 22 hours. How long would it take Paul and Matt to install the floor working together?
4 hours
9.9 hours
13.2 hours
30 hours
Answer:
9.9 hours
Step-by-step explanation:
The formula to determine the time together is
1/a+1/b = 1/c where a and b are the times alone and c is the time together
1/18 + 1/22 = 1/c
The least common multiply of the denominators is 198c
198c(1/18 + 1/22 = 1/c)
11c+ 9c = 198
20c = 198
Divide by 20
20c/20 =198/20
c =9.9
Answer:
B - 9.9 hrs
Step-by-step explanation:
took the test.
A pie is cut into 9 equal pieces. If all but 2 pieces are eaten, how much of the pie remains?
Answer:
is 7 pieces are remian
Step-by-step explanation:
9: total
2: eaten
so, 9-2 = 7 pieces?
Given: 3x+11=y, solve for x if y = 29
answer is 6
Step-by-step explanation:
3x+11=y
y=29
3x+11=29
3x=29-11
3x=18
x=18÷3
x=6
Answer:6
Step-by-step explanation:
3x+11=29
3x=29-11
3x=18
X=18/3
X=6
Find the missing side. Round your answer to the nearest tenth.
Answer:
[tex]sin\left(90\right)/x=sin\left(25\right)/16[/tex]
x = 37.85
Step-by-step explanation:
Deidre is planting tulips in her garden, and she has 44 red bulbs and 44 purple bulbs to plant in one row. What is the probability that she randomly plants the bulbs so that all 44 red bulbs are next to each other and all 44 purple bulbs are next to each other
Answer:
[tex]P=7.62*10^{-26}[/tex]
Step-by-step explanation:
From the question we are told that:
Available plants:
44 red bulbs
44 purple bulbs
Generally the equation for Total possible arrangement is mathematically given by
[tex]n= 88!/(44!*44!)[/tex]
[tex]n=2.6*10^{25}[/tex]
Since
Its either
All 44 red bulbs and All 44 purple bulbs next to each other in one row
OR
All 44 purple bulbs and All 44 Red bulbs next to each other in one row
Therefore
Probability is
[tex]P=\frac{2}{2.6*10^{25}}[/tex]
[tex]P=7.62*10^{-26}[/tex]
What is the correct answer?
Answer:
Option D
Only the equation in option D matches with the table
Answered by GAUTHMATH
At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 kmyh and ship B is sailing north at 25 kmyh. How fast is the distance between the ships changing at 4:00 pm
Answer:
the distance between the ships is changing at 21.4 km/h
Step-by-step explanation:
Given;
distance between ship A and ship B = 150 km
speed of ship, A = 35 km/h
speed of ship B = 25 km/h
at 4 pm, the time difference = 4 hours
let the distance between A and B = C
The position of A after 4 hours = 35 km/h x 4 h = 140 km
The distance covered by A, a = 150 km - 140 km = 10 km
The distance covered by B, b = 25 km/h x 4 h = 100 km
The distance between A and B;
c² = a² + b²
c² = 10² + 100²
c² = 10100
c = √10100
c = 100.5 km
The change in the distance between A and B is calculated as;
[tex]c^2 = a^2 + b^2\\\\2c\frac{dc}{dt} = 2a\frac{da}{dt} + 2b\frac{db}{dt} \\\\c\frac{dc}{dt} = a\frac{da}{dt} + b\frac{db}{dt} \\\\100.5(\frac{dc}{dt}) = -10(35) + 100(25) \\\\(the \ negative \ sign \ indicates \ decrease \ in \ distance \ of \ A \ from \ B \ with \ time)\\\\100.5(\frac{dc}{dt})= 2150\\\\\frac{dc}{dt} = \frac{2150}{100.5} \\\\\frac{dc}{dt} = 21.39 \ km/h\\\\\frac{dc}{dt} \approx 21.4 \ km/h[/tex]
Therefore, the distance between the ships is changing at 21.4 km/h
Help please. I need the answer
Answer:
y=-2/3x+6
Step-by-step explanation:
Graph it
Answer:
y= -2/3 x + 6
Step-by-step explanation:
1. In the graph, you can see the points (0,6) and (6,2)
2. Since you have all the available options, you can input both points into all equations.
3. In this case, the correct answer is y= -2/3 x + 6
You invested your summer earnings into and annuity from which you can draw expenses while you are at university. If you need to withdraw $1200 each month for 9 months of university, how much do you need to invest into an account, earning 6% per year, compounded semi-annually, in order to cover your expenses?
Answer:
10538.07
Step-by-step explanation:
find the effective semiannual rate: .06/2= .03
conver this into an effective monthly rate
[tex](1.03)^2=(1+i)^{12}\\(1.03)^{1/6}-1=i\\i=.0049386220312[/tex]
this is our montlhy effective rate. use this to calculate teh present value of 9 1200 dollars payments
[tex]1200(\frac{1-(1+.0049386220312)^{-9}}{.0049386220312})=10538.0729871[/tex]
which rounds to 10538.07
The invested amount would be $10538.52 in order to cover your expenses if you need to withdraw $1200 each month for 9 months of university.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt} \\\\\\rm A = P(1+\dfrac{r}{n})^{nt}+\dfrac{PMD((1+\dfrac{r}{n})^{nt}-1)}{\dfrac{r}{n}}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is or borrowed (in years)
It is given that:
You need to withdraw $1200 each month for 9 months of university,
The effective semiannual rate = 0.06/2 = 0.03
[tex]\rm i = (1.03)^{1/6} - 1[/tex]
i = 0.00493
The invested amount:
[tex]= 1200\dfrac{[1- (1 + 0.00493)^{-9}]}{0.00493}[/tex]
After simplification:
= $10538.52
Thus, the invested amount would be $10538.52 in order to cover your expenses if you need to withdraw $1200 each month for 9 months of university.
Learn more about the compound interest here:
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One leg of a right angle has a length of 3m. The other sides have lengths
what is Newton's Law of Cooling?
Answer:
Newton's law of coming states that the rate at which an object cools is proportional to the differences in temperature between the object and the object's surroundings.
Answer:
It is the rate of heat loss of a body that is directly proportional to the difference in the temperatures between the body and its surroundings. Q= h* A* (T(object) -T(environment) )
Steve thinks he can drive legally 30 minutes after he drinks 5 beers. The legal limit is BAC = 0.08. Give a 90% prediction interval for Steve’s BAC. Can he be confident he won’t be arrested if he drives and is stopped?
Answer: Hello your question has some missing data attached below is the missing data
How well does the number of beers a student drinks predict his or her blood alcohol content (BAC)? Sixteen student volunteers at Ohio State University drank a randomly assigned number of 12-ounce cans of beer. Thirty minutes later, a police officer measured their BAC. Here are the data. The students were equally divided between men and women and differed in weight and usual drinking habits. Because of this variation, many students don’t believe that number of drinks predicts BAC well.
answer:
prediction interval : (0.040 , 0.114)
Step-by-step explanation:
Given data:
Confidence level = 90%
Legal limit ( BAC ) = 0.08
solution
sample size = 16
Degree of freedom ( df ) = 14
critical t value = 1.761
X = 4.81
Σ(x-x)² (Sx) = 72.44
also standard error of estimates = 0.0204
Y= -0.01270 + 0.01796 * 5 = 0.077
given that ; the predicted value of Y at x = 5
Considering individual response Y
standard error = 0.0211
margin of error = 1.761 * 0.021 = 0.0371
Hence the limits of the prediction interval is :
Lower limit = 0.077 - 0.037 = 0.040.
Upper limit = 0.077 + 0.037 = 0.114
Finally
90% prediction interval = (0.040 , 0.114)
I don’t know what to do
Answer:
[tex]C=\pi d\\\\d=\frac{C}{\pi }[/tex]
Make d the subject:
C = πd
C/π = d
Your answer: d = C/π
In a recent survey for an upcoming city mayoral election, people were asked to name the political party they identified with and also the
the candidate they were going to vote for.
• Of the 150 people who identified themselves as Democrats, 133 said they would vote for the Democratic candidate. The rest said to
vote for the Republican.
. Of the 160 people who identified themselves as Republican, 142 said they would vote for the Republican candidate. The rest said ti
vote for the Democrat.
Complete the two-way frequency table for this situation.
B I u X
x
Font Sizes
A
А
E E 3 E3
Identify Party
Democrat Republican Total
Democratic
Voted
Republican
Total
Characters used: 89 / 15000
Submit
This question is solved using relative frequency concepts, finding the following two way frequency table, with the - separating the values:
0.4290 - 0.0540 - 0.4839
0.0581 - 0.4581 - 0.5161
0.4871 - 0.5121 - 1
-------------------------------------------------------------------------------
Relative frequency:
The relative frequency of a to b is given by a divided by b.
-------------------------------------------------------------------------------
Democratic:
Total of 150 + 160 = 310 voters.
Of the 150 Democrats, 133 voted for the Democrat and 150 - 133 = 17 voted for the Republican.
The frequencies are:
[tex]\frac{133}{310} = 0.4290, \frac{17}{310} = 0.0548[/tex]
Proportion of democratic voters is:
[tex]\frac{150}{310} = 0.4839[/tex]
Thus, the first line is: 0.4290 - 0.0540 - 0.4839
-------------------------------------------------------------------------------
Republican:
Of the 160 Republicans, 142 voted for the Republican and 160 - 142 = 18 voted for the Democrat.
The frequencies are:
[tex]\frac{18}{310} = 0.0581, \frac{142}{310} = 0.4581[/tex]
The proportion of republican voters is:
[tex]\frac{160}{310} = 0.5161[/tex]
Thus, the second line is: 0.0581 - 0.4581 - 0.5161
-------------------------------------------------------------------------------
Third line:
0.4290 + 0.0581 = 0.4871
0.0540 + 0.4581 = 0.5121
0.4839 + 0.5161 = 1
Thus, the third line is: 0.4871 - 0.5121 - 1
-------------------------------------------------------------------------------
Two-way frequency table:
The two-way frequency table is:
0.4290 - 0.0540 - 0.4839
0.0581 - 0.4581 - 0.5161
0.4871 - 0.5121 - 1
A similar question is given at: https://brainly.com/question/24337228
Answer:
Democratic 133 18 151
Republican 17 142 159
Total 150 160 310
Step-by-step explanation:
help i,m suck and i cant find the answer
in aremethic, variables look like
3. Seth invested money in two accounts, one paying 5% simple interest and the other paying
6% simple interest. The amount invested at 6% was $1000 more than the amount invested at
5%. He earned a total of $830 interest in 1 yr. Determine the amount invested in each
account.
Answer:
7000 and 8000 respectively
Step-by-step explanation:
Let x be invested in first account and x+1000 be invested in second account.
ATQ, 830=(5)*x/100+6*(x+1000)/100. Solving it will give us x=7000
The amount Seth invested at 5% is 7000 dollars and the amount Seth invested at 6% is 8000 dollars.
What is a percentage?A percentage is a value per hundredth. We can also convert percentages into decimals and fractions.
We know, SI = P×r×t/100, where SI = Simple interest, P = principle,
r = rate in % and t = time in years.
Assuming the total amount to be x dollars.
∴ x×5×1/100 + ( x + 1000)×6×1/100 = 830.
5x/(100) + (6x + 6000)/100 = 830.
5x + 6x + 6000 = 83000.
11x = 77000.
x = 7000.
Therefore the amounts are 7000 and (7000 + 1000) = 8000.
learn more about percentage here :
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Find length of AC? Help please
Answer:
D
Step-by-step explanation:
cos(theta) = B/H
cos(51)= AC/58
AC=36.5
Answer:
36.5 = AC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj side/ hypotenuse
cos A = AC / AB
cos 51 = AC /58
58 cos 51 = AC
36.50058 = AC
Rounding to the nearest tenth
36.5 = AC
A veterinarian is visited by many pets and their owners each day. Before the doctor attends to each pet, an assistant records information including the type, age, weight, and height of each pet. What are the individuals in the data set?
[What are the individuals in the data set?]
pets
types
weights
heights
I think it's pets, just posting so it helps other people with it. Someone make sure in the answers though.
Answer:
pets bcos a vetenarian is a doctor for animals and tha question also says their owners.
Ashley has a rectangle made out of paper that is 8 cm by12 cm. She folds it in half twice, first vertically and then horizontally. The new rectangle looks just like the original rectangle but smaller. What is the area of the new smaller rectangle in square cm
Answer:
[tex]Area =24cm^2[/tex]
Step-by-step explanation:
Given
[tex]L = 8cm[/tex]
[tex]W = 12cm[/tex]
[tex]r = 2[/tex] -- folded twice
Required
The area of the new rectangle
When the length was folder, the new length is:
[tex]l = L/2 = 8cm/2 = 4cm[/tex]
When the width was folder, the new width is:
[tex]w = W/2 = 12cm/2 = 6cm[/tex]
So, the new area is:
[tex]Area =l * w[/tex]
[tex]Area =4cm * 6cm[/tex]
[tex]Area =24cm^2[/tex]
Interpret the coefficient of determination. Choose the correct answer below. A. The coefficient of determination measures the percent of variation not explained by the multiple regression model. B. The coefficient of determination measures the percent of variation explained by the multiple regression model. C. The coefficient of determination measures the expected error of the predicted sales given a specific total square footage and number of shopping centers. D. The coefficient of determination measures the average predicted sales for the multiple regression model.
Answer:
B.The coefficient of determination measures the percent of variation explained by the multiple regression model.
Step-by-step explanation:
The answer to this question is option b because the coefficient of variation R² gives a measure of the variability that is ending y values or the dependent variables which can be explained in a multiple linear regression.
In simpler words, it is the percentage of proportion of variation in the dependent variable that can be predicted using the explanatory variables.
4. (08.02 MC)
Factor completely 2x3 + 10x2 + 14x + 70. (5 points)
(2x^2 + 14)(x + 5)
(x^2 + 7)(2x + 10)
2(x^3 + 5x2 + 7x + 35)
2[(x^2 + 7)(x + 5)]
Answer:
2[(x^2 + 7)(x + 5)]
Step-by-step explanation:
Note that the ratio of the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping, but first we can separate out the common scalar factor 2...
2x3+10x2+14x+70=
2(x3+5x2+7x+35)
2((x3+5x2)+(7x+35))
2(x2(x+5)+7(x+5))
2(x2+7)(x+5)
Answer:
The answer is D. 2[(x2 + 7)(x + 5)]
Step-by-step explanation:
Given coordinates A(3,3),B(2,5),C(4,3) complete transformation. Complete double reflection over the lines y=2 followed by y=0.
9514 1404 393
Answer:
A"(3, -1)B"(2, 1)C"(4, -1)Step-by-step explanation:
Reflection over 'a' then over 'b' will result in a translation of 2(b -a). Here, we have a=2, b=0, so the translation is 2(0-2) = -4. The reflection is over horizontal lines, so the transformation is ...
(x, y) ⇒ (x, y -4)
A(3, 3) ⇒ A"(3, -1)
B(2, 5) ⇒ B"(2, 1)
C(4,3) ⇒ C"(4, -1)
At the Olympic games, many events have several rounds of competition. One of these events is the men's 100100100-meter backstroke. The upper dot plot shows the times (in seconds) of the top 888 finishers in the semifinal round at the 201220122012 Olympics. The lower dot plot shows the times of the same 888 swimmers in the final round. A dot plot is divided into 2 parts labeled, Semifinal Round and Final Round. The horizontal axis is labeled, Time, in seconds, from 52 to 54, in increments of 0.10 second. The portion of the dot plot dedicated to Final Round has dots above the following points; 52.2, 52.3, 52.8, 53.1, 53.2, 53.3, 53.5, and 53.8. The portion of the dot plot dedicated to Semifinal Round has dots above the following points; 52.7, 53, 53.3, 53.3, 53.5, 53.5, 53.5, and 53.7. Which pieces of information can be gathered from these dot plots? (Remember that lower swim times are faster.)
Answer: None of the above.
Step-by-step explanation:
I got it right on khan. I’ll explain a little though. Semifinals median=47.05. Finals median=53.05. Therefore A is not and option and B is DEFINITLEY not an option. Sorry I’m not good at explaining
Answer:
None of the above
Step-by-step explanation:
Got it right on test
Please help me with this question
In 20P4 how many choices are
there for vice-president from a
state of four officers?
Note: The vice president is the second officer
to be elected.
Acellus
Explanation:
There are 20 choices for president, and 20-1 = 19 choices for vice president. You count down by 1 each time you fill a seat. So that means you'll have 19-1 = 18 choices for the third seat, and 18-1 = 17 choices for the fourth seat.
Find the surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet.
988 ft2
996 ft2
980 ft2
1000 ft2
Answer: 996 ft2
Step-by-step explanation:
Add up the area of all 6 sides of the prism:
(10 · 13) + (10 · 13) + (10 · 16) + (10 · 16) + (16 · 13) + (16 · 13)
= 130 + 130 + 160 + 160 + 208 + 208
=996 ft²
Answer:
B) 996 ft2
Step-by-step explanation:
Ted wanted to determine if one brand of paper towels (Brand A) was stronger than another brand (Brand B). He performed a study where he randomly selected 25 sheets from each of the two brands, placed each sheet in an embroidery hoop (and tightened the hoop), placed 30 drops of water on each paper towel, and placed weights on each sheet until the sheet broke. He recorded the maximum weight on the paper towel before it broke. Which of the following statements is correct?
A) A two-tail test will be performed since the alternative hypothesis contains a "less than"
B) A one-tail test will be performed since the alternative hypothesis contains a "not equal to".
C) A one-tail test will be performed since the alternative hypothesis contains a "less than".
D) A two-tail test will be performed since the null hypothesis contains a "not equal to"
E) A two-tail test will be performed since the alternative hypothesis contains a "not equal to".
Answer:
C) A one-tail test will be performed since the alternative hypothesis contains a "less than".
Step-by-step explanation:
Test may be categorized as being one tailed or two tailed depending on the inequality sign used when defining the hypothesis ` ; Hypothesis whereby the alternative hypothesis takes a not equal to (≠) are categorized as two talked as the direction of does not point to either the left or right. Conversely, alternative hypothesis which takes a less Than sign or takes a greater Than sign are classed as being one tailed as the they point to a specified direction..
For the scenario given : we are to test the claim that one is stronger than the other ;
For this knid if test it has been stated explicitly that one is greater than another ;
H0 : μ = μ
H0 : μ < μ
