How many baseballs with a diameter of 2.90inches, can fit into a box that is 48in x 40in x36in?
Answer:
5413 baseballs
Explanation:
Dimensions of the box = 48in x 40in x 36in.
The diameter of one baseball = 2.90 inches
Radius = Diameter ÷ 2 = 2.90 ÷ 2 =1.45 Inches
First, we find the volume of one of the baseball.
The baseball is in the shape of a sphere and:
[tex]\text{Volume of a Sphere}=\frac{4}{3}\pi r^3[/tex]Therefore, the volume of one baseball will be:
[tex]\begin{gathered} =\frac{4}{3}\times\pi\times1.45^3 \\ =12.77in^3 \end{gathered}[/tex]Next, we find the volume of the box.
[tex]\begin{gathered} \text{Volume of the box}=48\times40\times36 \\ =69120in\text{.}^3 \end{gathered}[/tex]Therefore, the number of baseballs that will fit into the box will be:
[tex]\begin{gathered} \frac{\text{Volume of the box}}{Volume\text{ of one baseball}}=\frac{69120}{12.77}=5412.7 \\ \approx5413 \end{gathered}[/tex]One serving of mikes crackers has 150 calories and a mass of 30 grams. how many calories are in y of the crackers
one serving has 150 calories and a mass of 30 g
1 gram= 150/30 = 5 calories
so y grams = y x 5 calories = 5y calories
Instructions: Create a table of values for the given function.
Given the function:
f(x) = 4x - 4
We re asked to create a table of values for thhe above function.
In order to create the tabe of value, we will use the x values give n in the table to replace the value of x in the function.
When x = -2
f(x) = 4(-2) - 4
= -8 - 4
= -12
When x = -1
f(x) 4(-1() - 4
= -4 - 4
= -8
When x = 0
f(x) = 4(0) - 4
= 0 - 4
= -4
When x = 1
f(x) = 4(1) - 4
= 4 - 4
= 0
When x = 2
f(x) = 4(2) - 4
= 8 - 4
= 4
So, let's complete the table:
x y
-2 -12
-1 -8
0 -4
1 0
2 4
Does the quadratic functionf(x) = 4x2 – 12x + 9 have one,two, or no real zeros? Utilize thequadratic formula to determinethe answer[?] real zero(s)-b Vb2 - 4acRemember the quadratic formula: x =
SOLUTION
Step1: Write out the equation
[tex]y=-2x^2-4x+2[/tex]Compare the equation with the general form of a quadratic equation
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{then } \\ a=-2,b=-4,c=2 \end{gathered}[/tex]Step2 Write out the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Step3: Substitute the parameters in step1
Answer correctly and I will give Brainly
Answer:
y= 5/6x+4
Step-by-step explanation:
you go up 5
over 6
so 5/6
then its already on positive 4 so its +4
Slope-intercept form is the form of a line where y equals the product of the slope and the input plus the y-intercept, or:
y = mx + b
[tex]m = \frac{y_2 - y_1}{x_2-x_1}\\m = \frac{9 - 4}{6-0}\\m = \frac{5}{6}[/tex]
b = 4
The final equation of the line is:
y = 5/6x + 4
-9(10-6r) help please
Given the expression :
[tex]-9\mleft(10-6r\mright)[/tex]using the distributive property to simplify the expression :
[tex]\begin{gathered} -9\mleft(10-6r\mright) \\ =-9\cdot10-9\cdot-6r \\ =-90+54r \end{gathered}[/tex]So, the result will be = -90 + 54r
There are 8 roses in a vase of 11 flowers. The rest are daisies.(a) What is the ratio of roses to daisies?0(b) What is the ratio of daisies to all flowers in the vase?0$ P
Let
x -----> number of roses
y-----> number of daisies
we have that
x=8
y=11-8=3
so
Part A
What is the ratio of roses to daisies?
ratio=x/y --------> ratio=8/3 or 8:3
Part B
What is the ratio of daisies to all flowers in the vase?
ratio=y/(x+y) -------> ratio=3/11 or 3:11
Leann determines the volume of the cylinder shown using the formula V=Bh.
We have that the base of the cylinder is a circle, and the area of a circle can be calculated with the following equation:
[tex]B=\pi\cdot r^2[/tex]In this case, we have the following:
[tex]\begin{gathered} \pi=3.14 \\ r=\frac{d}{2}=\frac{6}{2}=3 \\ \Rightarrow B=(3.14)(3)^2=(3.14)(3)(3) \end{gathered}[/tex]therefore, the area of the base is B=(3.14)(3)(3) = 28.26 cm^2
what is the dependent variable to the following equationy=3x+9
hello
to solve this question, let's identify the independent an dependent variable.
*independent variable: this is the variable that can stand alone on it own. It is usually equated with the rest of the equation.
in this question, the independent variable is y
*dependent variable: this is the variable that can't stand on it's own and also depends on the other side of the equation.
in this question, the dependent variable is x
A researcher wants to know if eating a mint affects whether people can distinguish between two popular orange juice brands. To conduct an experiment, the researcher places 50 participants in two groups. The treatment group will eat a mint before drinking a juice, while the control group will not eat a mint before drinking. Then the participants will guess the juice brand. To select the groups, the researcher labels each participant with a number and selects slips of paper labeled 1–50 from a bowl at random. The first 25 participants whose numbers are selected will be the treatment group, while the other 25 will be the control group.
The characteristics of the two groups
should be roughly equivalent because both groups will have 25 participants.
should be roughly equivalent because the participants were labeled and then randomly selected for the groups.
might not be roughly equivalent because one group may contain people that drink more juice than the other group.
might not be roughly equivalent because one group may contain more people that prefer a particular juice brand.
By the concept of probability D might not be roughly equivalent because one group may contain more people that prefer a particular juice brand.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty. A probability is a number that expresses the likelihood or chance that a specific event will take place. Probabilities can be stated as proportions between 0 and 1, or as percentages between 0% and 100%. The likelihood that something will happen is called the probability. the total number of conceivable outcomes. For instance, there is a 1 in 2 chance of tossing a coin and getting heads.
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4. Which of the following expressions will have the same value as the expression below? -7-(-5)A. -7+(-5)B. -7-5C. 7+(-5)D. -7+5
1) Let's operate this expression -7 -( -5)
-7 -( -5) The minus before the parentheses work as -1 x (-5)
-7 +5
-2
2) Examining each expression
a) -7+(-5) = -7 -5 = -12
b) -7-5= -12
c) 7-5 = 2
d) -7+5 = -2
3) So according to the options, the answer is D
-5ln+4l<15 true or false
So, for values lesser than -1 and greater than -7 this inequality is true.
In this inequality let's work applying the Absolute Value properties
1) -5ln+4l<15 Dividing both sides by 5
-|n+4|<3
|n+4|>-3
2) Applying Absolute value properties
|n+4|>-3
|n+4|>-3
n+4-4>-4-3
n>-4-3
n>-7
|n+4|>3
n+4>3
n+4-4>3-4
n>-1
3) So n < -1 and >-7
So for values lesser than -1 and greater than -7 this inequality is true.
find the solution of this system of equations2x-2y=149x+4y=37
2x-2y=14
9x+4y=37
Multiply the first equation by 2, and then add both :
4x-4y=28
+
9x+4y=37
_______
13x = 65
Divide both sides of the equation by 13
13x/13 = 65/13
x= 5
Replace x on any equation and solve for y:
2x-2y=14
2(5)-2y=14
10-2y= 14
Subtract 10 from both sides:
10-10-2y= 14-10
-2y= 4
Divide both sides by -2
-2y/-2 =4/-2
y= -2
Solution:
x=5
y= -2
what is the distance between points (5,2) and (1,-3) on a coordinate plane?A 3B 4.1C 8.5D 6.4
We are asked to find the distance between the following two points
[tex](5,2)\: and\: (1,-3)[/tex]Recall that the distance formula is given by
[tex]d=\sqrt[]{\mleft({x_2-x_1}\mright)^2+\mleft({y_2-y_1}\mright)^2}[/tex][tex]\begin{gathered} \mleft(x_1,y_1\mright)=\mleft(5,2\mright) \\ (x_2,y_2_{})=(1,-3) \end{gathered}[/tex]Let us substitute the given points into the above distance formula
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({1_{}-5_{}})^2+({-3_{}-2})^2} \\ d=\sqrt[]{({-4})^2+({-5})^2} \\ d=\sqrt[]{16^{}+25^{}} \\ d=\sqrt[]{41} \\ d=6.4 \end{gathered}[/tex]Therefore, the distance between the given two points is 6.4
Option D is the correct answer.
The dancer at (4,1) needs hair gel. She moved to the right on a slope of 8. Where can you deliver her hair gel? Will you please provide a graph and a written detailed explanation? Thank you!
It is given that the dancer is at the point (4,1), and then moved to the right on a slope of 8.
It is required to find the point she can be located by showing a graph with a detailed explanation.
Recall that the slope is the measure of the steepness of a line calculated by dividing the vertical change by the horizontal change.
Since the slope is given as 8, and this can be written as 8/1. It follows that the vertical change is 8 and the horizontal change is 1.
To find the new point add 1 to the x-coordinate (which represents the horizontal) and 8 to the y-coordinate (which represents the vertical):
[tex](4,1)\rightarrow(4+1,1+8)=(5,9)[/tex]Hence, the new position is at the point (5,9).
This is illustrated in the graph below:
The gel can be delivered at (5,9) as shown above.
(1/4) raised to the power of (x-2)=16I'll upload a picture
Answer
x = 0
Explanation
[tex]\begin{gathered} (\frac{1}{4})^{x-2}=16 \\ 4^{-1(x-2)}=4^2 \\ 4^{-x-2}=4^2 \\ \text{Equate both sides of the equation} \\ -x+2=2 \\ -x=2-2 \\ -x=0 \\ x=0 \end{gathered}[/tex]2. Ifa 28% tip is left on a restaurant bill of $80, find the total amount of the bill including
To find 28% of $80, we have to first convert 28% to decimal, then multiply $80 with it.
28% = 28/100 = 0.28
Now,
[tex]0.28\times80=\$22.4[/tex]The total amount of bill INCLUDING the tip is the total bill added to the tip amount. That is:
[tex]80+22.4=\$102.40[/tex]Total Amount:$102.40
Find mzi. 1 5 H 9 J Write your answer as an integer or as a decimal rounded to the nearest tenth.
Given
[tex]\begin{gathered} IH=5 \\ IJ=9 \end{gathered}[/tex]We can find the measure of I below.
Explanation
[tex]\begin{gathered} CosI=\frac{Adjacent\text{ }side}{Hypotenuse\text{ side}}=\frac{IH}{IJ}=\frac{5}{9} \\ I=Cos^{-1}\frac{5}{9} \\ I=Cos^{-1}0.98176 \\ I=56.3^{\circ\:} \end{gathered}[/tex]Answer:
[tex]I=56.3^0[/tex]Choose all properties that were used to simplify the following problem:
[38 + 677] + (-38)
[677 + 38] + (-38)
677 + [38 + (-38)]
677 + 0
677
additive identity
additive inverse
commutative property of addition
associative property of addition
distributive property
The property used in this problem are
commutative property of additionassociative property of additionadditive inverseadditive identityProperty of numbers.
We know that, there are four basic properties of numbers.
They are commutative, associative, distributive, and identity.
Given,
Here we have the problem
[38 + 677] + (-38)
[677 + 38] + (-38)
677 + [38 + (-38)]
677 + 0
677
Now, we need to identify all properties that were used to simplify the problem.
In the first step of the problem is,
[38 + 677] + (-38)
We have used the commutative property of addition to interchange the given numbers in the brackets,
[677 + 38] + (-38)
Now, we have to use the associative property of addition to group the numbers,
677 + [38 + (-38)]
Then we have to use the additive inverse, to get the value of brackets,
677 + 0
Finally we have to use the additive identity to get the result.
677
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55 pointsWhen the equation log. ( VnUn = 3 is solved for n in terms of a, where a > 0,a # 1, the resulting equation isn=adn = 03ооооn = 9n = 26Previous
please wait the question is downloading
the answer is
n=a^6A work shift for an employee at restaurant count of 8 hours what fraction of the employees work shift is represented by 2 hours
Let:
T = Total number of hours = 8
n = Number of hours = 2
Therefore, the fraction is:
[tex]\frac{2}{8}=\frac{1}{4}[/tex]Answer:
[tex]\frac{1}{4}[/tex]In the quadratic formula the expression b^2-4ac is called the _____1 maximum value 2 discriminant3 minimum value
ANSWER :
Discriminant
EXPLANATION :
b^2 - 4ac in quadratic formula determines if the roots are real or imaginary.
It is called discriminant.
9000 Employees 24 hours a day 365 days a week how many man hours a year
Answer: 2096 work hours per year
The graph shown is the solution set for which of the following
Given the graph of an inequality, you can identify that the boundary has the form of a "V". Therefore, you can identify that it is an Absolute Value Inequality.
By definition, an Absolute Value Equation written in Vertex Form is:
[tex]y=a|x-h|+k[/tex]Where "h" is the x-coordinate of the Vertex, and "k" is the y-coordinate of the Vertex. If "a" is negative, the graph opens down and if it is positive, the graph opens up.
In this case, the graph opens up, and you can identify in the graph that the Vertex is:
[tex]\mleft(-1,0\mright)[/tex]You can also identify that the boundary is formed by solid lines and the shaded region is below the boundary. This indicates that the inequality has this form:
[tex]\begin{gathered} y\leq a|x-(-1)| \\ \\ y\leq a|x+1| \end{gathered}[/tex]Notice that this inequality is given in the Answer choices:
[tex]y\le\mleft|x+1\mright|[/tex]In order to check it, let's choose two points on the shaded region:
[tex]\mleft(-2,-1\mright),(2,-2)[/tex]Substitute the coordinates into the inequality and evaluate. If they satisfy the inequality, then the are solutions to it:
- For the first point:
[tex]\begin{gathered} -1\le|-2+1| \\ \\ -1\le1\text{ (True)} \end{gathered}[/tex]- For the second point:
[tex]\begin{gathered} -2\le|2+1| \\ \\ -2\le3\text{ (True)} \end{gathered}[/tex]Hence, the answer is: Second option.
Round .00000572. Using single digit and power of 10
Given that
There is a number and we have to round it using the single digit and in powers of 10.
Explanation -
Whenever we convert a decimal number into powers of 10.
The power of 10 is always equal to the negative number of digits after the decimal.
Then, the number 0.00000572 can be written as0
[tex]0.00000572=5.72\times10^{-6}[/tex]Now we have to round off it to a single digit.
Then,
[tex]5.72\times10^{-6}\approx6\times10^{-6}[/tex]Final answer -
Therefore the final answer is 6 x 10^(-6)Which of the following correctly shows the next two terms after -40 in the pattern?-10, 20, -40,...А.80, 160B-2.5,5С60, -80D80, -160
In the pattern -10,20,-40 every next term is obtained by multiplication of -2.
So terms next to -40 is,
[tex]-40\cdot(-2)=80[/tex]Term next to 80 is,
[tex]80\cdot(-2)=-160[/tex]Thus next two terms od -40 are 80 and -160.
Option D is correct option.
Rebecca was comparing various sizes of canned applesauce. A 16-oz can of one brand costs $7.78 and a 12-oz can of the same brand costs $6.85. Find the savings to thenearest cent on buying 96 ounces of applesauce in 16-oz. cans compared to 12-oz. cans.$6.98$7.87$8.12$9.06None of these choices are correct.
To do the comparison, we need to calculate the cost of buying 96 ounces using both options.
For 16-oz can
The number of cans required to get 96 ounces will be
[tex]\begin{gathered} \frac{96}{16} \\ =6\text{ cans} \end{gathered}[/tex]The cost will be
[tex]\begin{gathered} 6\times7.78 \\ =46.68 \end{gathered}[/tex]The cost of 96 ounces of applesauce in 16-oz cans is $46.68.
For 12-oz can
The number of cans required to get 96 ounces will be
[tex]\begin{gathered} \frac{96}{12} \\ =8\text{ cans} \end{gathered}[/tex]The cost will be
[tex]\begin{gathered} 8\times6.85 \\ =54.80 \end{gathered}[/tex]The cost of 96 ounces of applesauce in 16-oz cans is $54.80.
The savings on buying in 16-oz cans will be
[tex]\begin{gathered} 54.80-46.68 \\ =8.12 \end{gathered}[/tex]The savings will be $8.12.
Write the equation for the given parent function and listed transformations, please.x^2, right 1, reflect across the x-axis, vertical shrink by 1/3
given the function
[tex]f(x)=x^2[/tex]right 1
[tex]f(x-1)=(x-1)^2[/tex]reflect accros x axis
[tex]-f(x-1)=-(x-1)^2[/tex]vertical shrink by 1/3
since it says a shrink
vertical compressions a<1
[tex]-\frac{1}{3}f(x-1)=-\frac{1}{3}(x-1)^2[/tex]then the equation is
[tex]-\frac{1}{3}\left(x-1\right)^{2}[/tex]You and a friend go to Efren’s Tacos and Burritos for lunch. You order 2 tacos and 2 burritos for a total of $9.00. Your friend orders 1 taco and 3 burritos for a total of $10.50. Create a system of equations and solve for how much each burrito costs and how much each taco costs.
Use b as your variable for burritos and t as your variable for tacos.
PLEASE SOMEONE ANSWER THIS FAST
Each burrito costs $3 and each taco costs $1.50.
How to calculate the equation?Let b = variable for burrito
Let t = variable for tacos.
The equation based on the information will be illustrated as:
t + 3b = 10.50 .... i
2b + 2t = 9 ..... ii
From equation i, t = 10.50 - 3b. Put this into equation ii
2b + 2t = 9 .
2b + 2(10.50 - 3b) = 9
2b + 21 - 6b = 9
Collect like terms
4b = 12
b = 12/4
b = 3
Burrito = $3
Since t + 3b = 10.50
t + 3(3) = 10.50
t + 9 = 10.50
t = 10.50 - 9
t = 1.50
Taco= $1.50
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Solve for x. x - 4= -12 A. -8 B. -16C. 16 D. 8
Given that;
[tex]x-4=-12[/tex]STEP 1: Add 4 to both sides of the equation;
[tex]x-4+4=-12+4[/tex]STEP 2: Simplify further;
[tex]x=-8[/tex]CORRECT OPTION: A