Option B: 5.25 is the length of XZ
Explanation:
The triangles PQR and XYZ are similar.
To determine the length of XZ, let us use the similarity theorem.
The theorem states that, "if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar".
Thus,
[tex]\frac{QR}{YZ} =\frac{PR}{XZ}[/tex]
Let us substitute the values from the diagram, we have,
[tex]\frac{4}{3} =\frac{7}{XZ}[/tex]
Multiplying both sides by 3, we get,
[tex]4 =\frac{21}{XZ}[/tex]
Thus,
[tex]XZ =\frac{21}{4}=5.25[/tex]
Thus, the length of XZ is 5.25
Hence, Option B is the correct answer.
3. Sandwich shop customers can choose the bread and meat they want.
The table shows the sandwiches that were sold on a given day.
White Bread Wheat Bread
Ham
22
24
Turkey
21
22
Tuna
What is the experimental probability that the next sandwich sold will be
tuna on wheat bread?
25
23
The experimental probability of the next sandwich sold being tuna on wheat bread is 23 out of 137 sandwiches sold, or approximately 0.168.
Explanation:The problem describes an experimental probability scenario where stopping after having recorded multiple outcomes does not affect the probability of the next outcome. Experimental probability is calculated by taking the number of times an event occurs and dividing it by the total number of trials.
In this case, a total of 137 sandwiches were sold (22 ham on white bread + 24 ham on wheat bread + 21 turkey on white bread + 22 turkey on wheat bread + 25 tuna on white bread + 23 tuna on wheat bread). Out of these, 23 were tuna on wheat bread.
The experimental probability of the next sandwich being a tuna on wheat bread is therefore 23/137, or approximately 0.168, if this same pattern continues.
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An 18% tip is given for a meal. What expression represents the total cost with tip
The total cost of a meal with an 18% tip is calculated by converting the tip to a decimal (0.18), multiplying it by the meal cost, and adding it to the original cost. For a $72 meal, the total with tip would be $84.96.
Explanation:To calculate the total cost of a meal including an 18% tip, you first convert the tip percentage to a decimal by dividing by 100. For an 18% tip, this gives you 0.18. Then, multiply the cost of the meal by this decimal to find the amount of the tip. Finally, add the tip to the original cost of the meal to find the total cost including the tip.
Example Calculation
If the cost of the meal is $72, the tip would be calculated as follows:
Convert the tip percentage to a decimal: 18% = 0.18Multiply the cost of the meal by the decimal to find the tip: 0.18 imes $72 = $12.96Add the tip to the original cost of the meal to get the total cost: $72 + $12.96 = $84.96Therefore, the total cost of the meal with an 18% tip would be $84.96.
8m^3 + 2m^3 + 49m^2 .
Answer:
[tex]m^2(10m+49)[/tex]
Step-by-step explanation:
[tex]Given \ \ 8m^3+2m^3+49m^2\\\\=m^3(8+2)+49m^2 \ \ \ \ \ \ \ (adding\ like\ terms)\\\\=10m^3+49m^2\\\\=10m\times m^2+49m^2\\\\=m^2(10m+49)[/tex]
52.3 is what percent of 1046
Answer:
it is 5%
Step-by-step explanation:
What is the constant of proportionality Y/X
Please help! I will give brainliest to CORRECT ANSWER!!
Answer:
3.5/1
Step-by-step explanation:
(0,0)
(3.5,1)
The scale on a map is 1 inch to 3 miles. If the distance between two points is 6 inches, what proportion should you use to find the actual distance?
Answer:
Step-by-step explanation:
=
Emily served 15.08 ounces of soup to her family of 4. How much soup did each person eat?
Answer: 3.77 ounces is the correct answer hope this helps
Answer:
Step-by-step explanation:
What is the median of the data: 76 54 92 88 76 88 75 93 92 68 88 76 76 88 80 70 88 72
Answer:
Median = 78
Step-by-step explanation:
Arrange the data in ascending order
54 68 70 72 75 76 76 76 76 80 88 88 88 88 88 92 92 93
Total number = 18
Median = average of middle terms = average of 9th and 10th term
= ( 76 + 80)/2 = 156/2 = 78
Identify the terms and like terms in the expression. 7+4p-5+p+2q
Final answer:
The terms in the expression are 7, 4p, -5, p, and 2q. The like terms in the expression are 4p and p. To simplify the expression, the like terms can be combined by adding their coefficients.
Explanation:
The terms in the expression are:
74p-5p2qLike terms in the expression are terms that have the same variable(s) raised to the same power. In this expression, the like terms are:
4p and pTo simplify the expression, we can eliminate the like terms by combining their coefficients. Adding 4p and p, we get 5p. Therefore, the simplified expression is:
7 + 5p - 5 + 2q
It is not possible to find the values of p and q without additional information.
write cos (19°) in terms of sine
Answer:
sin(71°)
Step-by-step explanation:
Sine lags behind cosine by 90°
In other word, cos(∅) = sin(90° - ∅)
cos(19°) = sin(90° - 19°)
= sin(71°)
Which inequality is equivalent to
−4t≥28
?
Answer:
t ≤ -7
Step-by-step explanation:
−4t≥28
−4/4 * t ≥ 28/4
−1 * t ≥ 7
-t ≥ 7
t ≤ -7
Alex is practicing his dives at a pool. He dives from the diving board that is 15 feet above the surface of water. His dive takes him 15 feet below the surface of water. Alex says that the two distances are opposites, so his total dive distance is 15+ -15 equals 0 feet. Are the two distances opposite? Is Alex his total dive distance correct? Explain your reasoning. Show your work. Use models, positive and negative numbers, and words to explain your answer.
Answer:
Alex is wrong in calculating his dive distance.
Actual distance of his Dive is 30 feet.
Step-by-step explanation:
Given:
Distance from where he dive from = 15 feet
Distance he reached after dive = 15 feet
Also Given:
Alex says that the two distances are opposites,
Also Total distance of dive according to Alex = 15 +-15 =0 feet
Solution:
Now we know that;
The diving board is 15 feet above the water level, and then he reached 15 deep in the water, but here it is important to know that even he is above the surface of the water he is diving in the water and then he reached 15 deep in the water.
So the two distances are in the same direction.
From above scenario we can say that
Total Distance of dive will be = 15 +15 =30 feet.
Hence We can say that Alex is wrong in calculating his dive distance. Actual Dive distance is 30 feet.
What is 24 % 0.4 in mathematics
Kathy found $0.29. Now she has a total of $1.00. How much money did Kathy have to start?
Answer:
71 cents
Step-by-step explanation: Well it would be $1.00 minus the 29 cents she just got So 100 minus 29 is 71 it’s easy to do it in your head just think of 100 minus 30 and it’s 70 then subtract 1 from 30 and add it to the 70
Answer:
$0.71
Step-by-step explanation:
make $1.00 "100"* and $0.29 "29"* and subtract 100 and 29 to get "71" then turn the "71" into $0.71**
* this is done by making it a percentage by moving two units to the right
** this is done by making it a decimal by moving to units to the left
which ordered pair are solutions to this equation? y=2x-3
To find the solutions to the equation y = 2x - 3, substitute different x-values and solve for y.
Explanation:The given equation is y = 2x - 3.
To find the ordered pairs that are solutions to this equation, substitute different x-values and solve for y.
Let's take the first ordered pair (294.5, 61) as an example:
Plug in x = 294.5 into the equation: y = 2(294.5) - 3Simplify: y = 589 - 3 = 586Therefore, the ordered pair (294.5, 61) is not a solution to the equation y = 2x - 3.
Repeat the same process for the other two ordered pairs to determine if they are solutions to the equation.
Find the sum of 2 4/5 + 1 7/15
Answer:
2.73
Step-by-step explanation:
2 4/5 + 17/15
8/5 + 17/15
By Elysium
(24 + 17)/15
41/15
2.73
Jeremy rides his bike at a rate of 15 miles per hour. Below is a table that represents the number of hours and miles Kevin rides. Assume both bikers ride at a constant rate. Which biker rides at a greater speed? Include all of your calculations in your final answer.
Time in hours (x) Distance in miles (y)
1.5 17.25
2 23
3.5 40.25
4 46
The correct answer would be, Jeremy rides at a greater speed than Kevin.
Step-by-step explanation:
Jeremy rides at a rate of 15 miles per hour
Kevin rides at a rate given in the table
Let Y be the distance traveled by Jeremy
And X be the number of hours
Then for Jeremy:
y/x = 15/1
=> y= 15 x
For Kevin:
(46-23)/(4-2)
= 23/2
= 11.5
So for Kevin, Y = 11.5 x
So when Jeremy's and Kevin's rates are compared,
15 > 11.5
which means Jeremy rides at a greater speed.
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What expression is equivalent to 7m+5.5m(2+m)
Answer: 12.5m(2+m)
Step-by-step explanation:
Whích strand of mRNA would be made during transcription using the DNA
strand shown below?
AGC GCT
O A. UCG CGU
O B. TCG CGA
O C. UCG CGA
O D. AGC GCT
In both DNA and RNA, pairs are formed between cytosine and guanine. In DNA, adenine pairs with thymine, but in RNA it pairs with uracil.
So the corresponding mRNA strand would be
C. UCG CGA
Answer:
UCG CGA
Step-by-step explanation:
Solve the system of linear equations bus graphing
y=1/2x+3
y= -2/3x-5
(1,3)
Answer:
The solution of [tex]y = \frac{1}{2} x + 3[/tex] and [tex]y = -\frac{2}{3} x - 5[/tex] is (-6.857, -0.429)
Step-by-step explanation:
The solution of y = 1/2 x + 3 and y = -2/3 x -5
is (-6.857, -0.429) . The solution is shown in the graph attached.
I don't understand this question I'm supposed to be graphing
x+y is equal or less than 3 plz help
y≤ 3 when x is 0 and x≤ 3 when y is 0
The graph is attached in figure below
Step-by-step explanation:
We need to graph x+y is equal or less than 3
Writing in mathematical form:
[tex]x+y\leq 3[/tex]
For solving we find x and y intercepts
The y-intercept can be found by putting x=0, y is :
[tex]0+y \leq 3\\y\leq 3[/tex]
y≤ 3 when x is 0
The x-intercept can be found by putting y=0, x is :
[tex]x+y \leq 3\\x+0\leq 3\\x\leq 3[/tex]
x≤ 3 when y is 0
Plotting these values on the graph:
The graph is attached in figure below
Keywords: Solving inequalities
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Sean is building a model ramp for his toy cars. The diagram shows the dimensions of the ramp.
Sean needs to figure out how much paint he needs in order to cover all of the sides of his ramp. What is the surface area of the ramp?
A) 102 cm2
B) 210 cm2
C) 258 cm2
D) 432 cm2
Option B is correct, the surface area of the ramp will be 210 square cm.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle.
Then the surface area of the triangular prism will be given as,
Surface area = 2 Area of triangle + 3 Area of rectangle
Surface area = (h x b) + (L₁ + L₂ + L₃) x W
Sean must determine how much paint he will use to cover all of the edges of his ramp.
The surface area of the ramp is calculated as,
SA = (8 x 6) + (5 + 6 + 7) x 9
SA = 48 + 18 x 9
SA = 48 + 162
SA = 210 square cm
Hence, the surface area of the ramp will be 210 square cm. Then the correct option is B.
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A function g(x) has x-intercepts at ( 1/2,0) and (6,0). Which could be g(x)?
g(x) = 2(x + 1)(x + 6)
g(x) = (x-6)(2x - 1)
g(x) = 2(x - 2)(x-6)
g(x) = (x + 6)(x + 2)
g(x) = (x-6)(2x - 1)
Step-by-step explanation:
when you expand, it will be 2x²-13x+6=0
when you factories the quadratic equations,
the answer will be 1/2 and 6
Answer:
g(x) = (x-6)(2x - 1)
Step-by-step explanation:
If the length of the radius of a circle is doubled, how does that affect the circumference and area?
The circumference will be doubled if radius is doubled
The area will increase four times if radius is doubled
Step-by-step explanation:
We will solve the question in two parts.
One for circumference and one for Area
Circumference:
The formula for circumference is given by:
[tex]C = 2\pi r[/tex]
Here r is the radius.
Doubling the radius means that new radius will be 2r
The new circumference will be:
[tex]C_N = 2\pi (2r)\\C_N = 2(2\pi r)\\C_N = 2C[/tex]
Hence,
The circumference will be doubled if radius is doubled
Area:
The area of circle is given by:
[tex]A = \pi r^2[/tex]
Putting radius equal to 2r
[tex]A_N = \pi (2r)^2\\A_N = \pi (4r^2)\\A_N = 4(\pi r^2)\\A_N = 4A[/tex]
Hence,
The area will increase four times if radius is doubled
Keywords: Circle, area
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5.3.4 Journal: Two-Variable Systems Elimination
I need urgent help
Answer:
1) X stands for individual acts and y, group acts. 2) Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). 3) [tex]S=\left \{ 5,10 \right \}[/tex]
Step-by-step explanation:
Completing with what was found:
1) Here is a summary of the scenario your classmate presented for the talent show:Main show The main show will last two hours and will include twelve individual acts and six group acts.Final show The final show will last 30 minutes and will include the top four individual acts and the top group act.The equations he came up with are: 12x+ 6y= 120, 4x+ y= 30
1. What do x and y represent in this situation?
X stands for individual acts and y, group acts.
Besides that, In the system of equation, they represent the time for x, and the time for y.
2. Do you agree that your classmate set up the equations correctly? Explain why or why not.
Yes, that's right. Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). Either for 120 minutes or 30 minutes length. And their sum totalizing the whole period.
3. Solving the system by Elimination
[tex]\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\:*(-3)\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ -12x+ -3y= -90\end{matrix}\right.\\3y=30\Rightarrow y=10\\4x+(10)=30\Rightarrow 4x=20\Rightarrow x=5\\S=\left \{ 5,10 \right \}[/tex]
Use symbols Replace each with a number to make /24 >1/4 > 4/ a true statement
The numbers that replaces each blank to make the inequality a true statement are 48 and 32. The new inequality is 48/24 > 1/4 > 4/32.
In Mathematics and Euclidean Geometry, an inequality is a relation that compares two or more numbers and variables in an algebraic equation based on any of the following inequality symbols:
Less than or equal to (≤).Greater than (>).Greater than or equal to (≥).Less than (<).Based on the information provided, we can logically deduce the following incomplete inequality;
_/24 > 1/4 > 4/_
In order to make the left-hand side of the inequality true, we must have a number that is greater 1/4 or 0.25;
48/24 = 2
48/24 > 1/4
2 > 0.25 (True)
In order to make the right-hand side of the inequality true, we must have a number that is less than 1/4 or 0.25;
4/32 = 0.125
1/4 > 4/32
0.25 > 0.125 (True).
In conclusion, any number that is greater than 1/4 would make the left-hand side of the inequality true while any number that is less than 1/4 would make the right-hand side of the inequality true.
Complete Question:
Use symbols. Replace each __ with a number to make _/24 >1/4 > 4/_ a true statement.
which graph represents decreasing distance with increasing time?
Answer: B, the second one
Step-by-step explanation:
In the first one your distance stays the same while your time increases. The second one the distance decreases as the time increases, the third one is a double increase and than the last one the distance stays the same as the time increases and than changes to Decrease increases
Answer:
B is the corrcet one! :)
Step-by-step explanation:
What is the value of x in the solution to the system
Answer:
whats the equation???
Step-by-step explanation:
Is x=4 solution to equation, x divided by 8 is 2? Show your work and explain how you know
Two trains, train A and train b Weigh a total of 354 tons. Train A is heavier than train b. The difference of their weights is 314 tons. What is the weight of each train
the weight of train A is 334 tons, and the weight of train B is 20 tons.
Let's denote:
- The weight of train A as x tons,
- The weight of train B as y tons.
We're given two pieces of information:
1. The total weight of both trains is 354 tons: [tex]\( x + y = 354 \)[/tex].
2. Train A is heavier than train B by 314 tons: [tex]\( x = y + 314 \).[/tex]
Now, we can set up a system of equations using these two pieces of information and solve for x and y.
From equation (2), we have:
[tex]\[ x = y + 314 \][/tex]
We can substitute this expression for x into equation (1):
[tex]\[ (y + 314) + y = 354 \][/tex]
Now, let's solve for y:
[tex]\[ 2y + 314 = 354 \][/tex]
[tex]\[ 2y = 354 - 314 \][/tex]
[tex]\[ 2y = 40 \][/tex]
[tex]\[ y = \frac{40}{2} \][/tex]
[tex]\[ y = 20 \][/tex]
Now that we have found the weight of train B, we can substitute this value into equation (2) to find the weight of train A:
[tex]\[ x = 20 + 314 \][/tex]
[tex]\[ x = 334 \][/tex]
So, the weight of train A is 334 tons, and the weight of train B is 20 tons.