There are 8 pints in 1 gallon, so 50×8 = 400 pints in 50 gallons.
400 × 3 red drops = 1200 red drops
400 × 2 blue drops = 800 blue drops
. Joan has a prescription for 100 Theophylline capsules. Joan informs the pharmacist that she only has enough money to purchase ¼ of the prescription today. How many capsules will Joan pay for today
100 * 4=
100*1/1*4=
100 / 4=
25
How do I check my answers to make sure it correct?
Answer:
25
Step-by-step explanation:
There are 100 capsules and she can only buy 1/4
Multiply 100 * 1/4
100 * 1/4 =
100/4
25
We can check by calculating how many she leaves at the store
100 * 3/4 =
300 /4 = 75
The ones she bought , plus the ones she left behind should be 100 capsules
25+ 75 = 100
100 = 100
Check
What value in the replacement set is a solution to this equation? 3(n+7)=48 Replacement set: {8, 9, 10} Drag the solution into the box.
Answer:
n = 9 is the value in the replacement set is a solution to the equation [tex]3(n+7)=48[/tex]
Step-by-step explanation:
Given an equation: [tex]3(n+7)=48[/tex] .....[1]
Replacement set: {8, 9, 10}
For n = 8
Substitute in equation [1], we get;
[tex]3(8+7)=48[/tex]
[tex]3(15)=48[/tex]
[tex]45=48[/tex] False.
Similarly, For n = 9
Substitute in equation [1], we get;
[tex]3(9+7)=48[/tex]
[tex]3(16)=48[/tex]
[tex]48=48[/tex] True.
for n = 10
Substitute in equation [1], we get;
[tex]3(10+7)=48[/tex]
[tex]3(17)=48[/tex]
[tex]51=48[/tex] False.
Therefore, the value in the replacement set is a solution to this equation [tex]3(n+7)=48[/tex] is, 9
Answer:
9
Step-by-step explanation:
Two trees have a bird on top of each. Distance between birdwatcher and first bird is 37 point 4 feet. Distance between each bird is 17 point 8 feet. Angle of depression between birdwatcher and first bird is unknown. a. 25.5° b. 64.5° c. 28.4° d. 61.6°
Answer:
64.5A
Step-by-step explanation:
Marvin has piece of chain that is 3_5 12 feet long. He uses 2 1_3 feet of the chain for his art project. How much chain does marvin have left? A 1__1 12 feet , B 1__2 12 feet , C 2__1 12 feet , D 2__2 12 feet
Answer:
The answer is A. 1 1/2
Step-by-step explanation:
You have 3 5/12 - 2 1/3
1/3 of 12 is 4.
So change 2 1/3 to 2 4/12
3 5/12 - 2 4/12 = 1 1/2
I hope this helps!
Cheers, July.
Angles 1 and 2 are supplementary.
Which equation represents the relationship between their measures?l?
Answer:
m∡1 + m∡2 = 180
Step-by-step explanation:
m∡1 + m∡2 = 180
This is because supplementary means they add up to 180°.
Which inequality is true?
Answer:
∠6 > ∠3 is TRUE.
Step-by-step explanation:
We know that acute angle is less than 90 degree while obtuse angle is more than 90 degree. By looking at the given angles, we can easily determine which angle is obtuse or acute. then we can decide which angle is bigger to find the answer.
∠10 > ∠7
FALSE;
Because∠10 is acute while ∠7 is obtuse.
------------
∠6 > ∠3
TRUE;
Because∠3 is acute while ∠6 is obtuse.
------------
∠9 > ∠11
FALSE;
Because∠9 is acute while ∠11 is obtuse.
------------
∠8 > ∠11
FALSE;
Because∠8 is acute while ∠11 is obtuse.
------------
Jordan needs 6 3/10 gallons of milk to make 4 1/2 gallons of ice cream. How much gallons of milk will Jordan need to make one gallon of ice cream.
Answer:
45/63
Step-by-step explanation:
6 3/10=63/10, 4 1/2=45/10,
(45/10)/(63/10)=45/63
The earth travels one full rotation around the sun 365.25. Ow many minutes does it take for the earth to travel one full rotation?
Find the x value so that the line through the points (x,-9) and (0,1) has a slope of -4
The x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4 is x = 5/2 or 2.5.
To find the x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4, we can use the slope formula:
slope = (change in y) / (change in x)
Given that the slope is -4 and the two points are (x, -9) and (0, 1), we can plug the values into the slope formula:
-4 = (-9 - 1) / (x - 0)
Now, simplify the equation:
-4 = -10 / x
Now, cross-multiply:
-4x = -10
Now, solve for x by dividing both sides by -4:
x = -10 / -4
x = 5/2
So, the x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4 is x = 5/2 or 2.5.
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Help me please Algebra Two!!
Answer:
a. -2, even mult. and 1, odd mult.
b.[tex](x+2)^2(x-1)[/tex]
c. Odd degree of 3 or higher, likely higher due to the turns in the graph.
Step-by-step explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity. Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial. The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.In this graph, there are two real zeros: -2,1
We can write them in intercept or factored form as (x-1) and (x+2).
Because the graph never crosses the x-axis at x=-2 the zero has an even multiplicity of at least 2. The opposite is true for x=1 because it crosses. Therefore it has an odd multiplicity of at least 1.
The graph is a sideways s shape and ends up so is positive.
This means the function has a degree of 3 or higher with the degree being odd.
BRAINLIEST AND 60 POINTS!!!!!!!
1.) A coin is flipped. What is the theoretical probability that the coin lands on tails?
2.) A six sided number cube is rolled. What is the theoretical probability that a number greater than 4 is rolled?
3.) 2 six-sided number cubes are rolled. What is the theoretical probability that the sum of the number cubes is 8?
Answer:
1. P ( tails) = 1/2
2.P (number greater than 4) = 1/3
3. P (2 die sum to 8) = 5/36
Step-by-step explanation:
A coin only has 2 possibilities, head or tails, and they are equally likely
So the probability of getting a tails is 1/2
P ( tails) = 1/2
A die has the numbers 1,2,3,4,5,6 . There are 2 numbers greater than 4. They are 5 and 6. So there are 2 of the 6 choices that work.
P (number greater than 4) = 2/6 = 1/3
See the dice chart
There are 36 possibilities when you roll the die.
There are 5 that sum to 8
P (2 die sum to 8) = 5/36
Answer:
Guy above is correct
Step-by-step explanation:
Terry has 3 gallons of fruit punch to serve at a party right and solve a proportion to determine how many quarts are in 3 gallons
In Ivy's neighborhood, 40% of the homes have a swimming pool. If there are 80 homes , how many have a pool
Answer:
32 houses will have a pool
Step-by-step explanation:
40% of 80 is 32
Find f(4) for f(x)=-1/2x+5
Answer:
HELLO :
f(4) = -1/2(4)+5 = -2+5=3
A plane flies at an average speed of 300 miles per hour the expreesion 300t gives the distance traveled by the plane in t hours find the distance traveled by the plane in 8 hours
It costs 3.24 for a pack of 12 pens. Find the unit price in dollars per pen. Round your answer to the nearest cent
QUESTION 34
What is the variance of the following data? If necessary, round your answer to two decimal places.
82, 44, 67, 52, 120
QUESTION 35
What is the variance of the following data? If necessary, round your answer to two decimal places.
10, 12, 15, 18, 11, 13, 14, 16, 19, 20
QUESTION 36
What is the standard deviation of the following data? If necessary, round your answer to two decimal places.
100, 140, 130, 180, 80, 160
QUESTION 34
We want to find the variance of [tex]82,44,67,52,120[/tex].
The variance can be calculated using the formula,
[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]
where
[tex]\bar X =\frac{82+44+67+52+120}{5}[/tex]
[tex]\bar X =\frac{365}{5}[/tex]
[tex]\Rightarrow \bar X =73[/tex]
This means that,
[tex]\sigma^2=\frac{(82-73)^2+(44-73)^2+(67-73)^2+(52-73)^2+(52-73)^2+(120-73)^2}{5}[/tex]
This gives us,
[tex]\sigma^2=\frac{(9)^2+(-29)^2+(-6)^2+(-21)^2+(47)^2}{5}[/tex]
[tex]\sigma^2=\frac{81+841+36+441+2209}{5}[/tex]
[tex]\sigma^2=\frac{3608}{5}[/tex]
[tex]\sigma^2=721.6[/tex]
QUESTION 35
We want to find the variance of [tex]10,12,15,18,11,13,14,16,19,20[/tex].
The variance can be calculated using the formula,
[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]
where
[tex]\bar X =\frac{10+12+15+18+11+13+14+16+19+20}{10}[/tex]
[tex]\bar X =\frac{148}{10}[/tex]
[tex]\fRightarrow \bar X =14.8[/tex]
This means that,
[tex]\sigma^2 =\frac{(10-14.8)^2+(12-14.8)^2+(15-14.8)^2+(18-14.8)^2+(11-14.8)^2+(13-14.8)^2+(14-14.8)^2+(16-14.8)^2+(19-14.8)^2+(20-14.8)^2}{10}[/tex]
This gives us,
[tex]\sigma^2=\frac{(-4.8)^2+(-2.8)^2+(0.2)^2+(3.2)^2+(-3.8)^2+(-1.8)^2+(-0.8)^2+(1.2)^2+(4.2)^2+(5.2)^2}{10}[/tex]
[tex]\sigma^2=\frac{23.04+7.84+0.04+10.24+14.44+3.24+0.64+1.44+17.64+27.04}{10}[/tex]
[tex]\sigma^2=\frac{105.6}{10}[/tex]
[tex]\sigma^2=10.56[/tex]
QUESTION 36
We want to find the variance of [tex]100,140,130,180,80,160[/tex].
The variance can be calculated using the formula,
[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]
where
[tex]\bar X =\frac{100+140+130+180+80+160}{6}[/tex]
[tex]\bar X =\frac{790}{6}[/tex]
[tex]\Rightarrow \bar X =131.67[/tex]
This means that,
[tex]\sigma^2=\frac{(100-131.6667)^2+(140-131.6667)^2+(130-131.6667)^2+(180-131.6667)^2+(80-131.6667)^2+(160-131.6667)^2}{6}[/tex]
This gives us,
[tex]\sigma^2=\frac{(-31.6667)^2+(8.3333)^2+(-0.6667)^2+(48.3333)^2+(-51.6667)^2+(28.3333)^2}{6}[/tex]
[tex]\sigma^2=\frac{10325}{9}[/tex]
[tex]\sigma^2=1147.22[/tex]
To find the variance of a set of data, find the mean, subtract the mean from each data point, square the differences, and find the average of the squared differences. The standard deviation is the square root of the variance.
Explanation:To find the variance of a set of data, follow these steps:
Find the mean of the data.Subtract the mean from each data point and square the result.Find the average of the squared differences.For the data set 82, 44, 67, 52, 120 (Question 34), the mean is 73, the squared differences are 81, 841, 36, 441, and 1849, and the average of the squared differences is 631.20, rounding to two decimal places.
For the data set 10, 12, 15, 18, 11, 13, 14, 16, 19, 20 (Question 35), the mean is 14.8, the squared differences are 23.04, 4.84, 0.64, 8.84, 12.96, 3.24, 1.44, 2.56, 19.36, and 29.16, and the average of the squared differences is 10.10, rounding to two decimal places.
To find the standard deviation of a set of data, take the square root of the variance. For the data set 100, 140, 130, 180, 80, 160 (Question 36), the variance is 9300, and the standard deviation is 96.49, rounding to two decimal places.
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Which inequality corresponds with the graph?
A) x > -2
B) x < -2
C) x ≤ -2
D) x ≥ -2
Answer:
D
Step-by-step explanation:
An inequality is an expression which means more than one number is a solution. We graph the solutions on a number line to show all possible values. We graph using circles and arrows.
Equal to and less/greater than are graphed with filled in circles on the value.Only less/greater than (not equal to) are graphed with open (not filled in) circles on the value.We draw an arrow the direction the solutions satisfy the inequality. Generally this is the direction the inequality itself points.This is a filled in circle on -2 so this is [tex]\leq or \geq[/tex]. This means only answers C and D are options.
Answer D points to the right.
Answer:
The answer is D
Step-by-step explanation:
MrsStrong was correct!!!! Thank you
A runner, training for a competition, ran on a track every day for 10 weeks. The first week he ran 8 kilometers each day of the week. The second week he increased his daily run by one lap (400 meters). The third week he increased again his daily run by one lap and so on. What is total distance he ran in 10 weeks?
Answer:
Total = 686000 meters for 10 weeks 7 days a week.
Step-by-step explanation:
Let's solve this by doing the increase on just 1 training day per week. Then we can find the grand total for 7 days a week by multiplying by 7
a = 8000
n = 10
d = 400
Sum = (a + L)*n/2
L = a + (n - 1)*dL = 8000 + (10 - 1)*400L = 8000 + 9*400L = 8000 + 3600L = 11600 metersSum = (8000 + 11600)*10/2
Sum = 19600 * 10/2
Sum = 98000 meters.
This total represents 1 training day a week.
The total amount is 7 times this figure.
Total = 7 * 98000 = 686 000 meters.
Justin and Mike are learning how to ski. Justin falls down every 30 feet. Mike falls down every 25 feet. If they both start skiing from the same point, how far is the first point where they will both fall down?
Answer:
150 feet
Step-by-step explanation:
in order to find the solution we have to take the L.C.M of 25 and 30
L.C.M of 25 and 30 is 150
so after 150 feet , they will both fall down
Answer: They will both fall down after 150 feet.
Step-by-step explanation:
Hi, to answer this question we have to find the least common multiple (LCM)
of 30 and 25:
To obtain the multiple of a number we have to multiply that number by another number (not zero) in the multiplication table order (by 1,by 2,by 3,etc)
Multiples of 30:30,60,90,120,150
Multiples of 2525,50,75,100,125,150
The LCM is a number that appears on both lists, and is the smallest.
They will both fall down after 150 feet.
Feel free to ask for more if needed or if you did not understand something.
Shemar tips at the rate of 75:5 waiters. How many waiters will he be tipping, if he can afford a $90 tip?
please help me with this question
Answer: 5, 3, [tex]\dfrac{1}{6}[/tex], D
Step-by-step explanation:
-5 < 0 so f(-5) = | -5 | = 5
-3 < 0 so f(-3) = | -3 | = 3
6 > 0 so f(6) = [tex]\dfrac{1}{6}[/tex]
graph D (since x can equal zero)
Please answer this question! 15 points and brainliest!
Answer:
-1< x< 3 x is an integer
Step-by-step explanation:
There are the dots on the number line. Three points are represented
x= 0,1,2
We want an inequality
-1< x< 3 x is an integer
If triangle ABC is similar to triangle DEF, which statement is true about the two triangles?
A.)Segment AB is congruent to segment DE, and angles C and F are congruent.
B.)Segment BC is proportional to segment EF, and angles A and D are congruent.
C.)Segment AB is congruent to segment DE, and angles C and F are proportional.
D.)Segment BC is proportional to segment EF, and angles A and D are proportional.
Answer:
B.)Segment BC is proportional to segment EF, and angles A and D are congruent.Step-by-step explanation:
If ΔABC and ΔDEF are similar, then
AB is proportional to DE
BC is proportional to EF
CA is proportional to FD
and
angles A and D are congruent
angles B and E are congruent
angles C and F are congruent
Answer:
B.)Segment BC is proportional to segment EF, and angles A and D are congruent.
Step-by-step explanation:
The graph of f(x)=sin(x) is transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right. What is the equation of the new function g(x) ?
Answer:
g(x) = 4 sin(x - 3)
Step-by-step explanation:
* Lets revise some transformation
- If the function f(x) translated horizontally to the right by h units, then
the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then
the new function g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then the new
function g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then the
new function g(x) = f(x) – k
- A vertical stretching is the stretching of the graph away from the
x-axis
- If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically
stretched by multiplying each of its y-coordinates by k.
- A vertical compression is the squeezing of the graph toward
the x-axis.
- If 0 < k < 1 (a fraction), the graph of y = k • f(x) is the graph of f(x)
vertically compressed by multiplying each of its y-coordinates by k.
* Lets solve the problem
∵ f(x) = sin(x)
∵ f(x) is stretching vertically by a factor of 4
∴ f(x) multiplied by 4
∵ f(x) is shifting 3 units to the right
∴ We will change x to (x - 3)
∵ The new function is g(x)
∴ g(x) = 4 sin(x - 3)
- The attached graph for more understand
f(x) is the red graph
g(x) is the blue graph
Answer:
g(x) = 4 sin(x - 3)
Step-by-step explanation:
The given function is:
f(x) = sin(x)
Stretching by a factor of 4:
A vertical stretch or compression of f(x) can be expressed as:
cf(x), where c is any constant
if c > 1, it indicates a stretch in vertical direction and if 0 < c < 1, it indicates a compression by a factor of c in vertical direction.
Since, given function is being stretched by a factor of 4, the transformed function will become:
4f(x)
Shifting by 3 units right:
A shift of f(x) to right can be obtained by subtracting c from every occurrence of x in f(x) , where c is the number of units f(x) is being shifted in right direction. Since in this case f(x) is shifted 3 units to right, the transformed function will be:
f(x - 3)
Applying both the transformations to f(x), we get g(x) as:
g(x) = 4 f(x - 3)
g(x) = 4 sin(x - 3)
Lynn has 8.58 in quarters and pennies. If she has eight times as many pennies as quarters, how many of each does she have
Answer:
10.82 is the answer
Step-by-step explanation:
On Saturday, a local hamburger shop sold a combined total of 520 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Saturday
Answer: 173
Step-by-step explanation: 173 x 3 = 519. 520-173 = 347
A knife is three times the cost of a spoon. 9 spoons and 12 knifes cost ?82.80 workout the cost of 1 knife.
Let S = spoon
Let K = knife
1 knife is thee times the cost of a spoon, so it would be 3S
Now you have 9S + 12K = 82.80
We can replace the K with 3S:
9S +12(3S) = 82.80
Simplify the left side:
9S + 36S = 82.80
Add:
45S = 82.80
Divide both sides by 45"
S = 82.80 / 45
S = 1.84
One spoon cost $1.84
We know one knife cost 3 times as much, so multiply the cost of a spoon by 3:
Knife = 1.84 x 3 = $5.52
Answer:
1.84 x 3 = $5.52
Which graph represents the polynomial function f(x)=x^3+3x^2-10x-24
[tex]f(x)=x^3+3x^2-10x-24\\\\y-intercept\ for\ x=0:\\\\f(0)=0^3+3(0)^2-10(0)-24=-24[/tex]
Answer:
The attached image shows he graph for given function.
Step-by-step explanation:
We are given the following expression in the question:
[tex]f(x) = x^3 + 3x^2-10x-24[/tex]
The zeroes of the given function can be calculated as:
[tex]x^3 + 3x^2-10x-24 = 0\\x = -4, x = -2, x=3[/tex]
Thus,the graph for the given function passes through the x-axis on the points (-4,0), (-2,0) and (3,0).
The function crosses the y-axis at the point (0,24)
The attached image shows the graph for given function.
Thus, the second option is the correct graph for given function.
Find all real numbers X such that 4x+2≥14 and -21x+1<22
[tex]\begin{cases}4x+2\ge14\\-21x+1<22\end{cases}[/tex]
In the first inequality, we have
[tex]4x+2\ge14\implies4x\ge12\implies x\ge3[/tex]
In the second, we have
[tex]-21x+1<22\implies-21x<21\implies x>-1[/tex]
The solution to the system is the intersection of these two intervals, which would be [tex]x\ge3[/tex].