A parallelogram has sides of length 16 units and 10 units. The shorter diagonal is 11 units. Find the measure of the longer diagonal. Round to 2 decimal places, if necessary.
The measure of the longer diagonal is 24.31 units
How to determine the longer diagonal?The side lengths are given as;
a = 16
b = 10
The shorter diagonal is represented as d1, and it is given as
d1 = 11
The longer diagonal is represented as d2, and it is calculated using
d1^2 + d2^2 = 2 * (a^2 + b^2)
Substitute the known values in the above equation
11^2 + d2^2 = 2 * (16^2 + 10^2)
Evaluate the sum
121 + d2^2 =2 * 356
Evaluate the product
121 + d2^2 = 712
Subtract 121 from both sides
d2^2 = 591
Take the square root of both sides
d2 = 24.31
Hence, the measure of the longer diagonal is 24.31 units
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In 5-card poker, the number of outcomes favorable to an event E is given in the table. Find the
probability of being dealt four of a kind or a a straight.
The probability of being dealt four of a kind or a straight is
(Round to 6 decimal places.)
Event E
Royal flush
Straight flush
Four of a kind
Full house
Flush
Straight
Three of a kind
Two pairs
One pair
No pair
Total
# of Outcomes Favorable to E
4
36
624
3744
5108
10,200
54,912
123,552
1,098,240
1,302,540
2,598,960
The probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
In 5-card poker, find the probability of being dealt the following hand. Refer to the table.
From the table:
Total number of outcomes = 2598960
Total number of favorable outcomes = 624 + 10200 = 10824
The probability of being dealt four of a kind or a straight
P = 10824/2598960
P = 0.00416
In percentage:
P = 0.416%
Thus, the probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.
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Fatima purchased a new mattress when it was on sale. The sale price was 34% less than the regular price. If the sale price was $371, what was the original price? (Round your answer to the nearest dollar).
Answer:
$580
Step-by-step explanation:
{371x(100-34)/100}+371=580
The original price (rounded to the nearest dollar) is $497.
Explanation:In this problem, we need to identify what's the original price of the new mattress.
Since we know that the sale price is $371 and is 34% lesser than the original price, we need to add 371 and 34%.
Grab a calculator and add 371 and 34%
we get:
371 + 34% = 497.14
Now round it to the nearest whole number, we get: 497
This is how the answer gets 497.
Hope this helps :)
A company makes Japanese-style lunch boxes called bento boxes. Each bento box is a cube with-foot-long edges. The company ships the bento boxes in a container in the shape of a rectangular prism that measures feet by feet by feet. A manager correctly finds the volume of the container using a formula. An employee double-checks the calculation by packing the container full of bento boxes. Use the drop-down menus to explain how both volume calculations compare. Click the arrows to choose an answer from each menu. The manager can find the volume of the container using the formula Choose... The employee correctly determines that the container can be filled with Choose... bento boxes. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the Choose... of one bento box. The volume found by using the formula is of bento boxes in the container. Y Choose... ▼ the volume of the total number
The volume of a container shows the amount of space that it has inside of it.
The use of bento boxes that has edges that are a foot long and the use of a rectangular-shaped container to ship it would have been more useful if the dimensions were provided.
How to calculate volume?Provided that the dimensions are provided, the formula that can be used to find the volume of a container is:
V = L × W × H
Where:
L= Length
W= Width
H= Height
It is worthy to note that your question is incomplete as you did not include the answer choices for how the manager found the volume of the container and other questions so a general overview was given.
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The manager can find the volume of the container using the formula lwh. The employee correctly determines that the container can be filled with 3 layers of 21 bento boxes. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the volume of one bento box. The volume found by using the formula is equal to the volume of the total numberof bento boxes in the container.
The mean, median, and mode of the five numbers 5,7,8,A,B are equal. Find all possible values of A+B
If the mean, median, and mode of the five numbers 5, 7, 8, A, and B are equal, the possible values of A+B are 20, where A is 8, and B is 12.
What are the measures of central tendency?The measures of central tendency include the mode, the median, and the mean.
Statistically, a central tendency is a typical value for a probability distribution.
The mode's value appears most often in a set of data values. The median is the middle value of a dataset. The mean represents the average.
To determine the possible values of A and B, we can start by finding the median value, which is the middle value in ascending order.
Data and Calculations:Median (Middle value) = 8
Mode = 8
Total value = 40 (8 x 5)
A = 8
B = 12.
Mean = 8 (40/5)
Thus, if the mean, median, and mode of the five numbers 5, 7, 8, A, and B are equal, the possible values of A+B are 20, where A is 8, and B is 12.
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The half-life of iron-52 is approximately 8.3 hours.How much of a 13 gram sample of iron-52 would remain after 8 hours? Round to three decimal places.
6.665 grams of the 13 grams remain after 8 hours.
How much of a 13 gram sample of iron-52 would remain after 8 hours?The decay equation for the 13 grams of iron-52 is:
[tex]N(t) = 13g*e^{(-ln(2)/8.3h)*t}}[/tex]
Where N is the amount of iron-52, and t is the time in years.
Where we used the fact that the half-life is exactly 8.3 hours.
Now, the amount that is left is given by N(8h), so we just need to replace the variable t by by 8 hours, so we get:
[tex]N(8h) = 13g*e^{(-ln(2)/8.3h)*8h}} = 6.665g[/tex]
So 6.665 grams of the 13 grams remain after 8 hours.
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What is the multiplicative rate of change of the function? which answer is it? These are the options 1/5, 2/5, 2, or 5
Find the total surface area.
answer choices
A. 731 cm²
B. 649 cm²
C. 900 cm²
D. 770 cm²
NEED HELP QUICK
Select the correct answer.
Firewood can be sold in cords. The wood is cut into equal lengths and stacked evenly in a rack.
Which geometric shape can be used as a model to calculate the volume of the cord of wood?
A.
cylinder
B.
pyramid
C.
rectangular prism
D.
cone
The volume of the cord of wood will be similar to the volume of a rectangular prism. Then the correct option is C.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
The rectangular prism is the most typical geometric form used to approximate the volume of a cord of wood.
The wood is evenly cut into identical lengths, and when stacked, it forms a rectangular prism.
Therefore, C. rectangular prism is the right response.
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Stillwater Junior high divides students into teams taught by a group of teachers. The table shows the number of students in each team.
The principal uses a computer to randomly select the name of a student from all the students in the school. With the computer program, it is possible to draw the name of the same student twice. If the principal selects the name of a student from the Voyagers on the first try, what is the probability she will draw the name of another student from the Voyagers on the second try?
A. 81/399
B. 41/200
C. 1/82
D. 21/100
Answer:
(A)81/399
Step-by-step explanation:
The probability that the Principal selects a voyager on the first try is
82/400
Since another student is to be selected, the total population has reduced by 1 and the number of voyagers has been reduced by 1.
Probability that another voyager is selected on the second try is
81/399
The correct answer is A.
can someone pls help me with this !
Using a line of best fit, the predicted tsunami speed for the following depths is given by:
a. 1151 km/h.
b. 572 km/h.
c. 130 km/h.
d. 122 km/h.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (depth, velocity) are given by:
(7000, 943), (4000, 713), (2000, 504), (200, 159), (50, 79), (10,36)
Inserting these points in the calculator, the velocity in function of the depth is:
v(d) = 0.12879d + 121.03448
Hence, the velocities are given as follows:
a. v(8000) = 0.12879 x 8000 + 121.03448 = 1151 km/h.
b. v(3500) = 0.12879 x 3500 + 121.03448 = 572 km/h.
c. v(70) = 0.12879 x 70 + 121.03448 = 130 km/h.
d. v(5) = 0.12879 x 5 + 121.03448 = 122 km/h.
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Find the total area of the shaded region.
The two curves intersect when [tex]y=0[/tex] and [tex]y=1[/tex]. Over the range [tex]0\le y\le1[/tex], the curve [tex]x=12y^2[/tex] lies above [tex]x=12y^3[/tex]. Hence the area of the shaded region is
[tex]\displaystyle \int_0^1 (12y^2 - 12y^3) \, dy = 4y^3 - 3y^4\bigg|_0^1 = (4-3)-(0-0) = \boxed{1}[/tex]
Evaluate each expression if a=2,b=-3,C=-1, and d=4
5+d(3b-2d)
Answer:
it's simple, put the values in the equation.
5 + d( 3b-2d) = 5 + 4( 3×-3 - 2× 4)
= 5 + 4( -9-8)
= 5+ 4 × -17
= 5-68 = -63 ans.
In the figure below, the segment is parallel to one side of the triangle. Find the value of x.
x+7
18²/3
0 24
025²/
16
22
Step-by-step explanation:
answer=18^2/3
according to the congruent triangles are present there.
so divide corresponding sides
In the similar quadrilaterals below, what angle corresponds to ∠C
HURRY PLEASE!!!
∠H
∠G
∠F
∠E
Answer:
angle G
Step-by-step explanation:
the quadrilateral did not change position or ration, it only shrank, so all the angles are in the same place and angle C = angle G
Answer:
2
Step-by-step explanation:
which theorem can be used to show that LJKL is the same as LMNP
a. AA similarity
b. SSS similarity
c. ASA similarity
d. SAS similarity
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each given function with the description of its graph.
y-intercept at (0, 2)
graph initially decreases slowly and then decreases rapidly
y-intercept at (0, 1)
graph initially decreases rapidly and then decreases slowly
y-intercept at (0, 1)
graph initially increases rapidly and then increases slowly
y-intercept at (0, 2)
graph initially decreases rapidly and then decreases slowly
y-intercept at (0, 1)
graph initially increases slowly and then increases rapidly
Y =
(4)*
y = 3²
y = 2(1) ²
The statements that applies are;
y-intercept at (0, 2), graph initially decreases rapidly and then decreases slowly.y-intercept at (0, 1), graph initially increases slowly and then increases rapidlyy-intercept at (0, 1) - graph initially decreases rapidly and then decreases slowly.What is the function about?The property of power function is known to be peculiar to the field of math. A power function is known to be one that is made up of a variable base that tends to be raised to a fixed power.
Note that the function is one that is made up of a constant base that is often raised to a variable power.
Following the property of power function, we can be able to obtain the information above.
Therefore, The statements that applies are;
y-intercept at (0, 2), graph initially decreases rapidly and then decreases slowly.y-intercept at (0, 1), graph initially increases slowly and then increases rapidlyy-intercept at (0, 1) - graph initially decreases rapidly and then decreases slowly.Learn more about function from
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Express (x + 3)² as a trinomial in standard
Answer:
x² + 6x + 9
Step-by-step explanation:
(x + 3)²
= (x + 3)(x + 3)
each term in the second factor is multiplied by each term in the first factor , that is
x(x + 3) + 3(x + 3) ← distribute parenthesis
= x² + 3x + 3x + 9 ← collect like terms
= x² + 6x + 9 ← in standard form
Help me with this please asap?!
Answer:
None of these answers are correct.
Step-by-step explanation:
[tex]QR=\frac{25+45}{2}=35[/tex]
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
By Trapezoid mid - segment theorem :
[tex] \qquad❖ \: \sf \:QR = \cfrac{MN+ OP}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR= \cfrac{25+ 45}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR = \cfrac{70}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR= 35 \: \: units[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
length of segment QR = 35Let f(x)=x²+kx+4 and g(x)=x³+x²+kx+2k, where k is a real constant.
Find the values of k such that the graph of f and the graph of g only intersect once.
The value of k such that the graph of f and the graph of g only intersect one is equal to 2.
The value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.
How to find the value of the constant k of a system of two polynomic equations
Herein we have a system formed by two nonlinear equations, a quadratic equation and a cubic equation. Given the constraint that both function must only intersect once, we have the following expression:
f(x) - x² - k · x = 4 (1)
g(x) - x² - k · x = x³ + 2 · k (2)
x³ + 2 · k = 4
x³ + 2 · (k - 2) = 0
If f and g must intersect once, then the roots must of the form:
(x - r)³ = x³ + 2 · (k - 2)
x³ - 3 · r · x² + 3 · r² · x - r³ = x³ + 2 · (k - 2)
Then, the following conditions must be met: - 3 · r · x² = 0, 3 · r² · x = 0. If x may be any real number, then r must be zero and the value of k must be:
2 · (k - 2) = 0
k - 2 = 0
k = 2
Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.
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Which figure does NOT belong?
Answer:
C (third figure from left)
Step-by-step explanation:
The spirals in the first, second, and fourth figures are all clockwise from the outer end, i.e., if you trace these three spirals with your finger from the outside to the inside, your finger will move clockwise.
However, if you did the same with the third figure, you would see that the spiral is anti-clockwise from the outside moving in.
Therefore, the third figure doesn't belong.
Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Claim: The mean age of students in a large statistics class is less than 31. A simple random sample of the students has a mean age of 30.4.
Choose the correct answer below.
A.
The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
B.
The sample is not unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
C.
The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
D.
The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
The correct option regarding the sampling is C. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
What do you mean sampling?Sampling is a process that is used in statistical analysis in which a predetermined number of observations are taken from a larger population
In this case, since the claim is mean pulse rate of students in a large statistics classes is greater than 72. The sample mean pulse rate was found to be 98.9 then the sample is not unusual if the claim is true. The sample is unusual if claim is false. Therefore there is sufficient evidence to support the claim.
The correct option is C.
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5=logb(32) what does b equal
Answer: 2
Step-by-step explanation:
When a^b = c, loga(c) = b
So b^5 = 32 and b is 2
HELP ME WITH THIS QUESTION AS SOON AS POSSIBLE
Answer:
the answer is 2880
Step-by-step explanation:
because you would use the formula (n - 2) x 180 which equals the sum interior angles of any polygon .
The letter n stands for number of sides so in this case you would do (18 - 2) x 180 so 16 × 180 = 2880
hope this helped :) pls ask if you need any more explanation .
pls give brainliest if you like my answer :)
Explain why organization was important in your thought process and calculation for an accurate solution. You should also reflect on how correct organization of a problem can help you in everyday life. Include real-world examples to support your response.
It should be noted that organization was important in the thought process and calculation for an accurate solution.
What is problem solving?It should be noted that problem-solving enables us to identify and exploit opportunities in the environment and exert control over the future.
In this case, problem solving skills and the problem-solving process are a critical part of daily life both as individuals and organizations
Also, good problem solving activities provide an entry point that allows all students to be working on the same problem.
In this case, the open-ended nature of problem solving allows high achieving students to extend the ideas involved to challenge their greater knowledge and understanding and problem solving develops mathematical power.
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5 4 3 2 1
O (4,1)
20
Do,1 of X is:
O (4,0)
O (5,1)
3
5
4
3
2
(3.2)
y
1234 5
(4,0 X
(2,-2)
Z
The image of X after the dilation is (a) (4, 0)
How to determine the image of X?From the figure, the coordinates of X are given as:
X = (4, 0)
The dilation is given as:
Do,1
This means that we dilate X across the origin by a scale factor of 1.
So, we have:
X' = 1 * (4 - 0, 0 - 0)
Evaluate
X' = (4, 0)
Hence, the image of X after the dilation is (a) (4, 0)
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TIME REMAINING
51:31
What are the factors of x2 – 100?
(x – 50)(x + 50)
(x – 10)(x + 10)
(x – 25)(x + 4)
(x – 5)(x + 20)
Answer:
(b) (x -10)(x +10)
Step-by-step explanation:
The factorization of the difference of squares is a special form:
a² -b² = (a -b)(a +b)
ApplicationYour expression is recognizable as the difference of squares:
x² -100 = x -10²
Using the above form, the factorization is ...
= (x -10)(x +10) . . . . . . . . matches the second choice
veronica and marty ride their hikes 46 miles every saturday. veronica rides at an average speed of 9.2 miles per hour
Answer:
5
Step-by-step explanation:
46/9.2 = 5
Circle B has a radius of 24 units, Circle E has a radius of 9 units, and segment CD = 4. Find segment A.F. Round your answer to the nearest tenth.
The length of segment A.F in the circles given is: 62 units.
What is the Radius of a Circle?A radius of a circle is half the diameter of a circle, which is a point from the center to any point on the circumference of the circle. This implies that any segment that is drawn from the center of a circle to any point on the circumference of a circle is a radius. Also, all radii of a circle are always congruent to each other.
Radius of circle B = AB = BD = 24 units [all radii of a circle are congruent to each other].
Radius of circle E = CE = EF = 9 units [all radii of a circle are congruent to each other].
CD = 4
DE = x
CD + DE = CE
Plug in the values into the equation
4 + x = 9
x = 9 - 4
x = 5
DE = 5
The length of segment DE is 5 units
A.F = AB + BD + DE + EF
Plug in the values into the equation
A.F = 24 + 24 + 5 + 9
A.F = 62 units.
Therefore, the length of segment A.F in the given circle is determined as: 62 units.
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HELP!!! (05.06 HC) During a laboratory experiment, a 2.36g sample of NaHCO3 was thermally decomposed to generate 1.57g of carbonic acid (H2CO3). Calculate the percent yield of carbonic acid for the reaction. Show all your work (10 points). NaHCO3 → Na2CO3 + H2CO3
The percentage yield of carbonic acid is 66 percent.
How to find percentage yield?The percentage yield of the carbonic acid can be found as follows:
NaHCO₃ → Na₂CO₃ + H₂CO₃
Hence, 2.36g sample of NaHCO₃ was thermally decomposed to generate 1.57g of carbonic acid (H₂CO₃)
Using law on conservation, the mass of the reactant is equals to the product.
Therefore,
percentage yield of carbonic acid = 1.57 / 2.36 × 100
percentage yield of carbonic acid = 157 / 2.36
percentage yield of carbonic acid = 66.2447257384
percentage yield of carbonic acid = 66 %
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