Jamie purchases 4 chocolate (3.57), 7 strawberry/vanilla, and 7 peanut butter cupcakes for an office party.
How to write the given information as an expression or an equation?The steps involved are:
Observe the given data and notice the variable termsUse operators like multiplication or fraction if it consists of terms like twice or thrice or one fourth etc.Use the operators like addition or subtraction (more or less/greater or smaller) in between those variablesSolve those equations for the required values.Calculation:Given that,
Jamie is ordering cupcakes for an office party.
There are three flavors - Chocolate, Strawberry/vanilla, and peanut flavors.
Jamie purchased a total of 18 cupcakes for $55.75
The cost for a single cupcake of each flavor is as follows:
Chocolate - $3
Strawberry - $2.75
Peanut - $3.50
Consider the number of cupcakes of each flavor as x, y, and z respectively.
So, the equations we can write from this data are,
x + y + z = 18 and
3x + 2.75y + 3. 50z = 55.75
But it is given that,
There are twice as many chocolate cupcakes purchased as peanut butter cupcakes.
So, z = 2x
Then the above two equations become,
3x + y = 18 and
10x + 2.75y = 55.75
By solving these two equations we get,
x = 3.57 ≅ 4
y = 7.28 ≅ 7
Since we know that z = 2x,
⇒ z = 2 × 3.57 = 7.14 ≅ 7
So,
There are 4 chocolate, 7 strawberry, and 7 peanut cupcakes.
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Which of these numbers is irrational?
-3.5
3.5
ОО
35
√5 help
Answer:
√5 is irrational
Step-by-step explanation:
A rational number is one that can be written exactly as an integer or ratio of integers. Written as a decimal number, it will have a finite number of digits, or a repeating decimal fraction.
ApplicationUsually, a number that can only be expressed exactly using a symbol will be irrational. For square roots, any root of an integer other than a perfect square will be irrational.
The integer 5 is not a perfect square. It is between the squares 2²=4 and 3²=9. The square root of 5 is irrational.
__
Additional comment
A reduced fraction whose denominator has factors other than 2 or 5 will translate to a repeating decimal. The number of repeating digits may be as many as 1 less than the denominator. For example, 1/19 has an 18-digit repeating decimal equivalent.
4. For a camping trip, each person packs 1.5 lb of food per day. Let p represent the number of people on the trip, and let f represent the total weight of food packed for each day. What is the independent variable in this relationship? Explain. I need this with explanation please:(
Use the diagram to complete the proof
The missing statements that completes the proof that proves that quadrilateral ACDB is a parallelogram is explained below.
What are the Properties of a Parallelogram?A quadrilateral that has the following properties is a parallelogram, in reference to the quadrilateral ACDB in the image given:
Opposite sides are congruent (AB ≅ CD and AC ≅ BD).Opposite angels are congruent to each other (∠A ≅ ∠D and ∠C ≅ ∠B).Consecutive angles are supplementary (m∠A + m∠C = 180°).Given that ΔCFD ≅ ΔBGA, the proof that quadrilateral ACDB is a parallelogram is given below:
Since we know that ΔCFD ≅ ΔBGA, therefore, CD ≅ BA because corresponding parts of congruent triangles are: congruent.
Since we also know that m∠DCA + m∠CAB = 180°, then we also know that both angles are: supplementary.
Transversal A.F cut the two lines, CD and BA, then the interior angles on the same side of the transversal are: supplementary, thus, we it implies we know that lines CD and BA would be: parallel.
Since one pair of sides (CD and BA) are both parallel and congruent, then we know that quadrilateral ACDB is a parallelogram.
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The perimeter of a rectangle is 64 feet. If one side of the rectangle has a length of 20 feet, how long is the other side?
Answer:
other side is 12
Step-by-step explanation:
Givens
Perimeter = 64 feet
L = 20
Formula
P = 2L + 2w Substitute Givens
64 = 2*20 + 2w Combine
64 = 40 + 2w Subtract 40 from both sides
64-40 = 40-40+2w Combine
24 = 2w Divide both sides by 2
24/2=2w/2
12 = w
Find the equation of a circle with center at (5, 6) and radius 8.
Answer:
(x - 5)^2 + (y - 6)^2 = 64
Step-by-step explanation:
Every circumference is in the form:
(x - xc)^2 + (y - yc)^2 = r^2
Where xc is the x of the center. Yc is the y of the center. r is the radius. We just plug in the values and we're done.
Answer:
[tex](x-5)^2+(y-6)^2=64[/tex]
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
center = (a, b)radius = rGiven:
center = (5, 6)radius = 8 unitsSubstitute the given values into the formula:
[tex]\implies (x-5)^2+(y-6)^2=8^2[/tex]
[tex]\implies (x-5)^2+(y-6)^2=64[/tex]
Therefore, the equation of a circle with the given values is:
[tex](x-5)^2+(y-6)^2=64[/tex]
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15-point question. Pls help
Answer:
44
Step-by-step explanation:
x + (22 - 13) = 53
x + 9 = 53
x = 44
Answer:
44
Step-by-step explanation:
x+(22-13)=53
x+22-13=53
x+9=53
x=44
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. A shaded polygon A B C D is graphed in an x y plane, where x axis ranges from 0 to 7 in increments of 1 and y axis ranges from 0 to 6 in increments of 1. The vertices are as follows: A (1, 1), B (2, 3), C (5, 4), and D (4, 2). Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image A′B′C′D′. The slope of C'D' is___ .
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.
Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).
Slope of CD = (2 - 4) / (4 - 5) = 2
Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.
Slope of C'D' = slope of CD (because preserves shape) = 2
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
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The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.
Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).
Slope of CD = (2 - 4) / (4 - 5) = 2
Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.
Slope of C'D' = slope of CD (because preserves shape) = 2
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
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Solve each system by elimination
Answer:
system of equation by elimination
1 write both equation in standard form
2 make the coefficient of one variable opposites
3 add the questions relating from step to eliminate one variable
4 solve for the remaining variable
5 substitute the solution from step for into one of the original equation
The geometry students have designed a hexagonal flowerbed for the Homes for
Humanity landscaping project. The shape indicates the color of the flowers. The
design is composed of two congruent rhombuses (blue), four congruent parallelograms
(red and white), and four congruent trapezoids (red and white). The circular area
surrounding the design is an existing rock bed.
The students have determined the following measurements of each figure:
the bases of the trapezoids are 6 ft and 8 ft,
• the heights of the trapezoid and the parallelogram are 3.5 ft each, and
• the horizontal distances between the left and right vertices of each rhombus is 2
ft.
Trapezoid
[tex]A=\frac{1}{2}(3.5)(6+8)=24.5[/tex]
Parallelogram
[tex]A=(3.5)(6)=21[/tex]
Rhombus
[tex]A=\frac{1}{2}(7 \cdot 2)=7[/tex]
Red Area
[tex]2(21)+2(24.5)=91[/tex]
White Area
[tex]2(21)+2(24.5)=91[/tex]
The circular area surrounding the design is an existing rock bed are 24.5, 21, 27, 91 and 91 ft sq.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
It is given the bases of the trapezoids are 6 ft and 8 ft,
The heights of the trapezoid and the parallelogram are 3.5 ft each, and the horizontal distances between the left and right vertices of each rhombus is 2 ft.
Trapezoid
Area = 1/2(3.5)(6 + 8)
Area = 24.5
Parallelogram
Area = 1/2(3.5)(6)
Area = 21
Rhombus
Area = 1/2(7)(2)
Area = 7
Red Area
Area = 2(21) + 2(2.4)
Area = 91
White Area
Area = 2(21) + 2(2.4)
Area = 91
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Given AB=15cm,BC=20cm.Find AB correct 3 significant
(question refer to a triangle ABC which is right -angled at C)
The length of AB is 25 units
How to determine the length AB?The given parameters are
AC = 15 cm
BC = 20 cm
The triangle is right -angled at C.
So, we have:
AB^2 = AC^2 + BC^2
This gives
AB^2 = 15^2 + 20^2
Evaluate
AB^2 = 625
Take the square roots
AB = 25
Hence, the length of AB is 25 units
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2x-3y=1 2x+3y=2 describe the process of using addition to show that the lines are intersecting
Two lines in a plane can intersect,overlap or be parallel.When two lines intersect they have a common point which lies on both line.This is called solution of the two simultaneous equation which when graphed represent straight lines. Adding the two equations uses Elimination method to solve for x and y. The x and y value obtained is the common point lying on both the lines.
2x - 3y = 1
+ 2x + 3y = 2
4x =3 Or x=3/4
Substituting x value in any of the two-equation we can find the corresponding y value .
2x-3y=1
2(3/4) - 3y =1
Solving for y
y= 1/6
The point of intersection of the two lines is ( 3/4, 1/6)
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A restaurant has the following items on its three-course menu.
List all the possible three-course meals that could be ordered, assuming diners must order one meal from each category.
Starters:
Salad
Garlic bread
Mains:
lamb
pizza
desserts:
cookie
brownie
Answer:
salad, lamb, cookie
salad, pizza, brownie
garlic bread, lamb, cookie.
garlic bread, pizza, brownie
What are the inputs of the following function?
{(-3, 2), (-4, 2), (8,3), (7, 1)}
A. {-4, -3, 7, 8}
B. {1, 2, 3, 7, 8}
C. {1, 2, 3}
D. {-4,-3, 1, 2, 3, 7, 8}
Answer:
A. {-4, -3, 7, 8}
Step-by-step explanation:
The ordered pairs representing a function are always written ...
(input, output)
InputsThe set of inputs for the given function is the list of first-numbers of the ordered pairs. Those numbers are -3, -4, 8, 7. When we express them as a set, we like to have the elements of the set in increasing order:
inputs = {-4, -3, 7, 8} . . . . . . matches the first choice
In how many ways can max select 3 toppings from 10 available toppings for his
12. pizza?
Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order. Combinations can be confused with permutations.
Thus number of ways in which Max can select 3 toppings from 10 available toppings for his pizza is 10C3
=[tex]\frac{10!}{7!3!}[/tex]
= [tex]\frac{8.9.10}{3!}[/tex]
= 120
Thus Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.
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solve -9 2/7 - (-10 3/7)
Instructions: Find the surface area of the figure below. Round your answers to the nearest tenth, if necessary.
The surface area of the figure given is of: 61.3 yd².
What is the combined surface area of a figure?The combined surface area of a figure is the area of each figure.
This figure is composed by:
A circle of radius 3 yd.A triangle with base 6 yd and one leg 11.4 yd.The area of the circle is given as follows:
[tex]A = \pi r^2 = \pi \times 3^2 = 9\pi[/tex]
For the triangle, we need to find it's height, which is the leg of a right triangle, in which one of the sides is 3 and the hypotenuse is 11.4, hence:
h² + 3² = 11.4²
[tex]h = \sqrt{11.4^2 - 3^2}[/tex]
h = 11 yd.
Hence the area of the triangle is:
A = 0.5 x 6 x 11 = 33 yd²
The surface area of the figure is:
9pi + 33 yd² = 61.3 yd².
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number 68 is increased by 43%
Answer:
68 increased by 43% is 97.24.
Step-by-step explanation:
Multiply 68 by 1.43.
68×1.43=97.24
The answer is 97.24.
Hope this helps!
Answer:
97.24 Absolute change, And the actual difference is 97.24 - 68 = 29.24.
Step-by-step explanation:
Design your own statistical question that you can ask at least twenty different people. Keep in mind that the question should result in a variety of different numerical answers. What is your statistical question?
Ask at least twenty different people (classmates, family, friends, neighbors, teammates, etc.) your statistical question and record their answers. Describe the people you asked and how you gathered your data.
Organize and list your numerical data in order from least to greatest. Then, determine the values of the five-number summary for your set of data.
Use your five-number summary to create and upload a box plot that displays your data set.
A statistical question you can ask at least 20 different people can be: "How many pets do you have?"
An hypothetical data for the number of pets 20 sixth graders have has been given and the box plot that displays the data set is in the image below.
What is a Statistical Question?A statistical question can be defined as a question that can be answered by collecting a variety of numerical answers that vary. Examples of statistical questions include:
What are the age of students in my class?What are the heights of students in a class?A statistical question you can ask at least 20 different people can be: "How many pets do you have?"
Below is the hypothetical questions that can be assumed you'd get from two people:
0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 5, 5
Description of the people you asked can be: 20 sixth graders in your school.
How you gathered your data can be: Asking them to fill a questionnaire or by interview.
The numerical data from least to the greatest, hypothetically would be:
0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 5, 5
The five-number summary for the hypothetical data would be:
Minimum: 0 (least data point)
Quartile Q1: 1 (middle of the first half of the data distribution)
Median: 1.5 (center of the data)
Quartile Q3: 2.75 (middle of the second half of the data distribution)
Maximum: 5 (greatest data value).
Using the five-number summary generated, the box plot that displays the data set is shown in the image attached below.
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A cyclist rides her bike at a rate of 21 kilometers per hour. What is this rate in kilometers per minute? How many kilometers will the cyclist travel in 20 mins. Don’t round your answers
Answer:
0.35 km per minute, 7 km in 20 minutes
Step-by-step explanation:
1 hr = 60 minutes
21 km per 60 minutes = 21/60 = 0.35 km per minute
In 20 minutes: 0.35*20 = 7 km
Shara is building a birdhouse. She cuts a 6-foot-long board into sections that are each 1/3 foot long. How many sections of the board will Shara have when she is finished cutting?
A 2
B 6 1/3
C 10 1/3
D 18
Answer:
D
Step-by-step explanation:
Dividing by a fraction is the same as multiplying by its reciprocal.
6 ÷ 1/3
= 6 x 3/1
= 6 x 3
= 18
The number of sections of the board Shara has when she is finished cutting is 18 sections.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Length of the board = 6 feet
Length of the section = 1/3 feet
The number of 1/3 feet sections.
= 6 ÷ 1/3
= 6 x 3
= 18
Thus,
Shara when she is finished cutting will have 18 sections.
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Dion is 4 years older than Agustina. In 3 years the sum of their ages will be 46. How old is Dion now?
Answer:
22
Step-by-step explanation:
Dion (d) is 4 years older than Agustina (a)
d=a+4
In 3 years the sum of their ages will be 46
d+3+a+3=46
d+a+6=46
d+a=40
d=40-a
d=a+4
a+4=40-a
2a=36
a=18
Plug a back in
18+4=d
22=d
d=22
Sorry if this was a little long.
Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start.
The solution of the given exponential equation is 0.688.
Given that Mike is working on solving the exponential equation 37ˣ = 12.
An exponential equation is an exponential equation where the power (or) part of the exponent is a variable.
firstly, we have to slve this equation is by converting it to logarithmic form. Any exponential equation can be transformed into an equivalent logarithmic equation as follows:
aˣ = y
logₐy = x
Now, we will apply this transformation to our equation and we get
log₃₇12=x
Further, we will apply the change of base formula so that solution is written in terms of base 10 logs:
x=log12/log37
So, this is an exact answer to given equation, but we can simplify it further by using decimal approximation of it using a calculator. Remember that these logs are base 10:
x≈1.079/1.568
x=0.688
Hence, the solution of the given exponential equation 37ˣ=12 is 0.688.
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HALP URGENT PLS im dum
x =x=x, equals
^\circ
∘
Answer:
x = 55°
Step-by-step explanation:
That square box indicates a right angle.
A right angle is 90°.
We know that angle x and the 35° angle are making up this 90° angle together.
So, the equation to show what this ship looks like is the following:
[tex]x+35=90[/tex]
This is a simple equation, that if we solve, we get:
[tex]x=55[/tex]
So, x is 55°.
Considering the angle of the ray, it is found that the value of x is of x = 55º.
What is the angle of the ray?The ray has an angle of 180º. It is composed by:
Angle x.An angle of 35º.An angle of 90º.Hence:
x + 35 + 90 = 180
x = 180 - 125
x = 55º.
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If you could help me on 1 and 2 that would be great!!!
The conversion of the vectors into coordinate notation rule are as follows;
(-3, 1) ==> (x-3, y+1)(4, -7) ==> (x+4, y-7)What are the coordinate notation form of the given vectors?It follows from the task content that the vectors given in the task content can be converted to coordinate notation form by mapping x and y to their respective transformation units. It therefore follows that the coordinate notation form of the vectors are;
(-3, 1) ==> (x-3, y+1)(4, -7) ==> (x+4, y-7)Read more on coordinate notation;
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Factor x4 + xy3 + x3 + y3 completely. Show your work. Hint: First factor out a monomial. x4 + xy3 + x3 + y3 =
Answer:
[tex]x^{3} ( x + 1 ) + y^{3} (x+1)\\= (x+1)(x^{3} + y^{3})[/tex]
Answer:
Step-by-step explanation:
YOU PLUS ALL OF THEM
If my savings of $x grows 10% each year. how much will I have in: 2 years
The amount I'll have in two years at the growth rate described is; $1.21x.
How much will I have in 2 years?Since it follows that the savings grow by 10% each year, it can be concluded that the growth factor is; 110% = 1.1
Hence, in two years, we have;
= $x × (1.1)²
= $1.21x.
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Answer:
1.21x
Step-by-step explanation:
on rsm it says its correct
Find the missing segment in the image below.
Answer:
10.
Step-by-step explanation:
6/9 = x/15
9x = 6*15
9x = 90
x = 10.
Answer:
10
Step-by-step explanation:
[tex]\frac{6}{15} =\frac{x}{x+15}[/tex]
[tex]6(x+15)=15x[/tex]
[tex]6x+90=15x[/tex]
[tex]90=15-6x[/tex]
[tex]90=9x[/tex]
[tex]x=90/9= 10[/tex]
Hope this helps
If A, B, C, and D, are the only possible outcomes of an experiment, find the probability of D using the table below. . Group of answer choices 1/4 3/7 4/7 1/7
Using it's concept, the probability of D is 4/7.
What is a probability?
A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, A, B and C all have a probability of 1/7. The sum of all probabilities is of 1 = 100%, hence:
[tex]3 \times \frac{1}{7} + P(D) = 1[/tex]
[tex]P(D) = 1 - \frac{3}{7}[/tex]
[tex]P(D) = \frac{4}{7}[/tex]
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If a peregrine falcon dove at its maximum speed for half a mile to catch prey, how many seconds would the dive take
The dive of the Peregrine falcon took 7.5 seconds
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed X Time
Assuming the top speed of a Peregrine falcon is 240mph.
Distance travelled by the Peregrine falcon = 0.5 miles
By using the formula we get
0.5 = 240 x time
time = [tex]\frac{1}{480}[/tex] hours
time = [tex]\frac{3600}{480}[/tex] seconds = 7.5 seconds
∴ The dive of the Peregrine falcon took 7.5 seconds
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Let k be the largest integer such that 343/7^k is an integer. What is the remainder when 343/7^k is divided by 7
Answer:
1
Step-by-step explanation:
The given ratio will be the remaining factor of 343 after factors of 7 have been removed. The value of interest is that factor, modulo 7.
Factors of 343343 = 7·7·7 = 7³
RatioThe value of k is the power of 7 in the factorization of 343, so we have ...
k = 3
and ...
343/7³ = 1
RemainderThe remainder when this ratio is divided by 7 is ...
1 mod 7 = 1
The remainder when 343/7^k is divided by 7 is 1.