Combine like terms:
3 x 2 - 2x + 7 - 57 - 4x + 10
-34 - 6x
What is the distance between the points (7, −10) and (−8, −10)?
Answer:
15
Step-by-step explanation:
Using the distance formula
Answer:
15
hope this helps please make mine the brainliest
Three people each select a letter of the alphabet. What is the probability that they select the same letter?
Final answer:
The probability that three people independently select the same letter of the alphabet is 1/676.
Explanation:
The question asks about the probability that three people select the same letter of the alphabet independently. Since there are 26 letters in the alphabet, the first person can pick any letter with a probability of 1 (they are sure to pick some letters). The second person must pick the same letter as the first, which has a probability of 1/26. Similarly, the third person also has a probability of 1/26 to pick the same letter as the first two. To find the combined probability for all three events happening in sequence (all three picking the same letter), we multiply the individual probabilities: 1 * (1/26) * (1/26) = 1/676.
Find the experimental probability, P(tails), based on the data collected.
tosses: 80
tails: 40
(A)1/2
(B)1/4
(C)2/3
(D)1/3
Answer:
(A) 1/.2.
Step-by-step explanation:
Experimental Probability = the total number of tails / total number of tosses
= 40 / 80
= 1/2 (answer).
Answer:
The answer is (A) 1/2 its correct on gradpoint
three classes at a junior high school raised money to buy new computers
•ms moore’s class raised $249.00
•ms aguilars class raised $396.62 more than ms.moores class
•mr.barrys class raised $430.43 less than ms.augilars class
what is the total amount of money raised by all three classes
Answer:
$1109.81
Step-by-step explanation:
$249.00 +$369.62= $618.62(ms. aguilars class)
$618.92-$430.43= $188.19(mr. barry's class)
$249.00+$618.62+$188.19=$1109.81(complete answer of all 3 classes combined)
Answer:
The final amount is $1109.81
Step-by-step explanation:
In order to find the total amount, start with the know amount, which is Ms. Moore's class. Her class raised $249. Now we can use that to find the amount from Ms. Aguilar's class.
$249 + $396.62 = $645.62
Now we can use the amount from Ms. Aguilar's class to find the amount from Ms. Barry's class
$645.62 - $430.43 = $215.19
Now we can add the three amounts together to find the total amount.
$249 + $645.62 + $215.19 = $1109.81
for a field trip the school bought 67sandwiches for 6.60 each and 59 bags of chips for 3.25 each . how much did the school spend in all
Answer:663.95$
Step-by-step explanation:
Answer:
633.95
Step-by-step explanation:
The ratio of the height of two similar pyramids is 4:7. The volume of the smaller pyramid is 1,331cm, to the nearest whole number, what is the volume of the larger pyramid ?
Answer:
The volume of the larger pyramid is equal to [tex]7,133\ cm^{3}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z----> the scale factor
In this problem, the ratio of the height is equal to the scale factor
[tex]z=\frac{4}{7}[/tex]
step 2
Find the volume of the larger pyramid
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z----> the scale factor
x----> volume of the smaller pyramid
y----> volume of the larger pyramid
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{4}{7}[/tex]
[tex]x=1,331\ cm^{3}[/tex]
substitute
[tex](\frac{4}{7})^{3}=\frac{1,331}{y}\\ \\(\frac{64}{343})=\frac{1,331}{y}\\ \\y=343*1,331/64\\ \\y=7,133\ cm^{3}[/tex]
Which function is graphed below ?
ANSWER
Option B is correct
EXPLANATION
On the interval,
[tex]x \: < \: 2[/tex]
The function is a straight line graph with x-intercept
[tex]x = 1[/tex]
and y-intercept
[tex]y = - 2[/tex]
The equation of this line is
y=2x-2
On the interval, 2≤x≤5,
The equation is the constant function, y=4
On the interval x>5,
The equation is y=x+1
The correct choice is B.
Explain why the definitions of each rigid-motion transformation needs to be more precise than just referring to them as slides, flips and turns.
Answer:
Step-by-step explanation:
The definitions of rigid-motion transformations need to be precise as they entail more than physical descriptions of motions. They have unique mathematical definitions and are important for understanding and interpreting real-world movements and physical phenomena.
Explanation:The definitions of each rigid-motion transformation, namely slides (translations), flips (reflections), and turns (rotations), need to be more precise because they are not solely about the physical manifestation of the motion. These transformations have distinct mathematical underpinnings. For instance, a translation involves moving the figure along a specified direction and distance in a straight line, without changing the orientation of the figure. A reflection involves 'flipping' the figure over a line of reflection, altering its orientation but not its shape or size. A rotation involves turning the figure around a specified point for a given angle.
Moreover, in both rotational and translational motion - two forms of rigid-body motion, there are accurate variables such as displacement, velocity, and acceleration related to translational motion and the corresponding angular variables in rotational motion. These specific definitions are crucial for the mathematics behind movement and interpreting the world around us. Understanding such concepts can also aid in studying physical phenomena as diverse as a spinning ballet dancer or a rotating planet.
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What is the expression equivalent to? Screenshots attached. Please help, ASAP! Important.
Answer:
Choice C is the correct solution
Step-by-step explanation:
We can split up the terms under the cube root sign to obtain;
[tex]\sqrt[3]{32}*\sqrt[3]{x^{8} }*\sqrt[3]{y^{10} }\\\\\sqrt[3]{32}=\sqrt[3]{8*4}=\sqrt[3]{8}*\sqrt[3]{4}=2\sqrt[3]{4}\\\\\sqrt[3]{x^{8} }=\sqrt[3]{x^{6}*x^{2}}=\sqrt[3]{x^{6} }*\sqrt[3]{x^{2} }=x^{2}*\sqrt[3]{x^{2} }\\\\\sqrt[3]{y^{10} }=\sqrt[3]{y^{9}*y }=\sqrt[3]{y^{9} }*\sqrt[3]{y}=y^{3}*\sqrt[3]{y}[/tex]
The final step is to combine these terms;
[tex]2\sqrt[3]{4}*x^{2}*\sqrt[3]{x^{2} }*y^{3}*\sqrt[3]{y}\\\\2x^{2}y^{3}\sqrt[3]{4x^{2}y }[/tex]
Write all the factors of 16
Use commas to separate them.
Factors of 16 :
1, 2, 4, 8, 16
1,2,4,8,16
Method16 is a composite number and it is 4 squared. 16= 1x16,2x8 or 4x4. So all the factors of 16 is 1,2,4,8,16
How much is 3788 plus 83762
Answer:
87550
Step-by-step explanation:
Answer:
3788 + 83762 = 87,550
Use substitution method for y=10x-9 and y=x+18
Answer:
x=3
y=21
Step-by-step explanation:
To use substitution method, first we need to decide which variable solve first, either x or y.
Here we decide to start by 'y' using equation y=x+18, which is already solved for 'y'
That same equation is then substitute into the first equation:
x+18= 10x-9
From here, we isolate 'x' variable and grouping terms, we have this:
27=9x
Resulting x=3
Now, we can use the above result in the second equation (y=x+18)
Leading to y=3+18=21.
Mrs Johnson has $110 to spend on parking will cost $12 and admission tickets will cost $140 per person including tax
The answer is Ms Hernandez can bring up to 6 people to the zoo.
x - the number of people that she can bring to the zoo
The parking will cost $7: a = 7
Admission tickets will cost $15.50 per person: b = 15.50x
She can spend on parking and admission tickets $100:
a + b ≤ 100
a = 7
b = 15.50x
7 + 15.50x ≤ 100
15.50x ≤ 100 - 7
15.50x ≤ 93
x ≤ 93 / 15.50
x ≤ 6
250 female nurses to 100 male nurses what is the ratio of male nurses to female nurses
Answer:
2:5
it may be faster to google it
Answer:
Required ratio is 2:5.
Step-by-step explanation:
Given that number of female nurses = 250
Given that number of male nurses = 100
Now we need to find about what is the ratio of male nurses to female nurses.
So we just need to divide number of male nurses by the number of female nurses. That means divide 100 by 250. We get:
[tex]\frac{male}{female}=\frac{100}{250}[/tex]
[tex]\frac{male}{female}=\frac{10}{25}[/tex]
[tex]\frac{male}{female}=\frac{2}{5}[/tex]
Hence required ratio is 2:5.
Select the representation that does not change the location of the given point. (4, 110°)
Question 6 options:
(4, 290)°
(-4, 200)°
(4, 470)°
(-4, 470)°
Answer:
(4,470°)
Step-by-step explanation:
The representation that does not change the location of (4, 110°) in polar coordinates are all points that are coterminal with the given point.
The only point among the given options that is coterminal with (4, 110°) is (4, 470)°
The two points have the same magnitude and 470°-360°=110°.
Since 110° is coterminal with 470° and the two points have the same magnitude with the same sign, the two points represent the same location in polar coordinates.
The correct choice is (4,470°)
In the polar coordinate system, the point (4, 470°) is the representation that does not change the location of the given point (4, 110°). We obtain this by adding 360° to the given angle.
Explanation:This question is based on the concept of polar coordinates. Polar coordinates represent a point in space by specifying its distance from a reference point, usually the origin, and the angle made with the positive x-axis. In polar coordinates, (r, θ), 'r' represents the distance and 'θ' is the angle.
Given point is (4, 110°). We can notice that by adding or subtracting multiples of 360° from the angle, we are not changing the location of the point. So, if we add 360° to the 110°, we will obtain 470°. Hence, the point that represents the same location is (4, 470°).
The point (-4, 200°) represents the point in the opposite direction and the points (4, 290°) and (-4, 470°) change the angle beyond or below what is allowable without changing the point's location.
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three vertices of a square are (-1, 2), (-1, 8), and (5,2) what is the fourth vertex of the square
A. (-5, 2)
B. (5, 8)
C. (2, 8)
D. (2, -5)
Answer:
The correct answer option is B. (5, 8).
Step-by-step explanation:
We are given the following coordinates of the vertices of a square and we are to find the coordinates of its fourth vertex:
[tex] ( - 1 , 2 ) , ( - 1 , 8 ) , ( 5 , 2 ) [/tex]
We know that all four sides of the square are equal so the vertices are equidistant from each other.
So the fourth vertex will be (5, 8).
The answer is b. (5,8)
two lines intersecting at a right angle
Answer:
Perpendicular Lines
Answer:
Step-by-step explanation:
Perpendicular Lines
Which will hold more cake batter the rectangular pan or two round pans
Answer:
I don't know the size of the pans, but I'd probably say the rectangle ones.
Step-by-step explanation:
Y'know, you have to calculate volume and all that put based on the info given rectangular pans usually hold more...although there are two round pans...please add some numbers to clarify!
Frank got a gift for his sister and put it in a shoebox.
Now, he wants to wrap it with wrapping paper.
If the length of the shoebox measures 9 in, the width measures 4 in, and the height measures 3 in, how much wrapping paper does he need to cover the shoebox?
Answer:
150 square inch
Step-by-step explanation:
you want to calculate each rectangle area individually then add all together
A = lw
1st one....9*4 = 36 sq. in
2nd one..4*3 = 12 sq. in
3rd one...9*3 = 27 sq. in
4th one...4*3 = 12 sq. in
5th one...9 *4 = 36 sq. in
6th one...9*3 = 27 sq. in
____________________
add all = 150 sq. in.
For what natural values of n:
is the difference (2−2n)−(5n−27) positive?
The expression (2−2n)−(5n−27) is not positive for any natural values of n, because when simplified, the inequality n < −(25/7) suggests n would need to be a negative value, which is not possible for natural numbers.
To determine for which natural values of n the expression (2−2n)−(5n−27) is positive, we must solve for the values of n that make the expression greater than zero. Simplifying, we get:
2 − 2n − 5n − 27 > 0
−7n − 25 > 0
Since we have a negative coefficient for n, as n increases, the value of the left side of the inequality decreases. To find the values of n that satisfy the inequality, we isolate n:
−7n > 25
n < −(25/7)
Considering n must be a natural number (positive integer), there are no natural values of n that satisfy the inequality, as natural numbers are always non-negative, and our inequality requires n to be less than a negative number.
A bicyclist covered 5/7 of his route and an additional 40 miles. He has yet to cover 118 miles less than 0.75 of his route. How long is his route in miles?
Answer:
6 miles
Step-by-step explanation:
Let the route length be r. The distance the cyclist has already covered is then (5/7)r + 40. This plus 0.75r - 118 must = r, the length of the entire route.
Then:
(5/7)r + 40 + (3/4)r - 118 = r
The LCD of the fractions 5/7 and 3/4 is 28. We thus have:
(20/28)r + 40 + (21/28)r - 118 = r, or
(41/28)r - 78 = (28/28)r
Combining the r terms, we get 13r = 78, and so r = 78/13 = 6.
The cyclist's bike route is 6 miles long.
Answer:
168 miles
Step-by-step explanation:
Please help me answer these
Answer:
1 is 27
Step-by-step explanation:
A survey of all teachers at a school found that the mean time planning for their classes is 54 minutes a day. Is the mean time a parameter or a statistic?
Answer:
Statistic
Step-by-step explanation:
You are asking more than one people/persons so it would be statistic.
ED decides to include more fruit in his diet he goes to the grocery store over the weekend and buys six apples six oranges six avocados the total cost is 19.50 write 3 Equations
Answer:
x = (19.5 - 6y - 6z) /6
y = (19.5 - 6x - 6z) /6
z = (19.5 - 6x - 6y) /6
Step-by-step explanation:
Let the Apples be X
Oranges be Y
Avocados be Z
Total cost of the Fruits = 19.5
So the equation would be as follows:
6x + 6y + 6z = 19.5
for Apples, equation would be:
6x= 19.5 - 6y - 6z
x = (19.5 - 6y - 6z) /6
For Oranges, the equation would be:
6y= 19.5 - 6x - 6z
y = (19.5 - 6x - 6z) /6
For Avocados, the equation would be:
6z= 19.5 - 6x - 6y
z = (19.5 - 6x - 6y) /6
Answer:
simple answer
Step-by-step explanation:
Let x be the cost of one apple, y the cost of one orange, and z the cost of one avocado.
The first weekend, Ed buys 6 of each fruit and pays $19.50: 6x+6y+6z=19.5
The second weekend, Ed buys 12 apples, 2 oranges, and 1 avocado and pays $9.50: 12x+2y+z=9.5
The third weekend, Ed buys 2 apples, 4 oranges, and 5 avocados and pays $14: 2x+4y+5z=14.
Please help me answer this!
Answer:
option B
[tex]\frac{280}{\sqrt{L}\sqrt[3]{P}}[/tex]
Step-by-step explanation:
Step 1
S varies inversely of the cube root of P
s [tex]\alpha[/tex][tex]\frac{1}{\sqrt[3]{P} }[/tex]
s = [tex]\frac{k}{\sqrt[3]{P} }[/tex]
Step 2
S varies inversely with square root of L
s[tex]\alpha\frac{1}{\sqrt{L} }[/tex]
s = [tex]\frac{k}{\sqrt{L} }[/tex]
Step 3
Jointly
s = [tex]\frac{k}{\sqrt{L} \sqrt[3]{P} }[/tex]
Step 4
Plug values given in the question to find constant of proportionality
7 = [tex]\frac{k}{\sqrt{100}\sqrt[3]{64}}[/tex]
7 = k /(10)(4)
7 = k/40
k = 280
Step 5
General formula will be
s = [tex]\frac{280}{\sqrt{L}\sqrt[3]{P}}[/tex]
A salesperson earns a salary of $700 per month plus 2% of the sales. Which inequality correctly represents the total sales if the salesperson is to have a monthly income of at least $1800?
Answer:
55000
Step-by-step explanation:
1800 - 700 = 1100
1100 / 0.02 = 55000
please answer the question in the screenshot below
Answer:
x = 20
∠B = 92
∠C = 40
Step-by-step explanation:
im pretty sure
Answer:
x = 20. ∠B = 92° and ∠C = 40°
Step-by-step explanation:
Angles of a triangle are ∠A = 48°, ∠B = (6x - 28)° and ∠C = (2x)°
Since sum of all the angles of the triangle is 180°
So ∠A + ∠B + ∠C = 180°
48° + (6x - 28)° + (2x)° = 180°
48 + 6x - 28 + 2x = 180
8x + 20 = 180
8x = 180 - 20
8x = 160
x = [tex]\frac{160}{8}=20[/tex]
Now ∠B = (6x - 28) = 6×20 - 28
∠B = 120 - 28 = 92°
And ∠C = 2x° = 2×20 = 40°
Therefore, x = 20. ∠B = 92° and ∠C = 40° is the answer.
The point (2, 3) is on the terminal side of angle Θ, in standard position. What are the values of sine, cosine, and tangent of Θ?
Answer:
sin Ф = 3/√13; cos Ф = 2/√13; and tan Ф = 3/2
Step-by-step explanation:
Let's assume we're limiting ourselves to Quadrant I.
Start with the tangent function. tan Ф = opp / adj.
In this case opp = 3 and adj = 2.
The length of the hypotenuse is found using the Pythagorean Theorem and is √(3² + 2²) = √13.
Then sin Ф = opp / hyp = 3/√13 or 3√13/13
and
cos Ф = adj / hyp = 2/√13 or 2√13/13
and (as before)
tan Ф = opp / adj = 3/2
sin(θ) is approximately 0.832
cos(θ) is approximately 0.555
tan(θ) is 1.5
The given parameters are;
The location of point (2, 3) = The terminal side of angle θ in standard position
The required parameters;
sin of θ, cosine of θ, and tangent of θ
Strategy;
Draw angle θ on the coordinate plane based on definition showing point (2, 3) on the terminal side and find the required trigonometric ratio
Standard position is the position of an angle that has the vertex at the
origin, the fixed side of the angle is on the x-axis and the terminal side
which defines the angle is drawn relative to the initial fixed side to form
the given angle either clockwise or anticlockwise
We have the following trigonometric ratios with regards to the reference angle;
[tex]sin\angle X = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}[/tex]
The hypotenuse length = √(2² + 3²) = √13
Therefore;
[tex]\mathbf{sin( \theta)} = \dfrac{3 - 0}{\sqrt{13} }= \dfrac{3}{\sqrt{13} } = \mathbf{\dfrac{3 \cdot \sqrt{13} }{13}}[/tex]
[tex]\mathbf{sin( \theta)} \ is \ \mathbf{\dfrac{3 \cdot \sqrt{13} }{13}} \approx 0.832[/tex]
[tex]cos\angle X = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}[/tex]
Therefore
[tex]\mathbf{cos( \theta)} = \dfrac{2 - 0}{\sqrt{13} }= \dfrac{2}{\sqrt{13} } =\mathbf{ \dfrac{2 \cdot \sqrt{13} }{13 }}[/tex]
[tex]\mathbf{cos( \theta)} \ is \ \mathbf{ \dfrac{2 \cdot \sqrt{13} }{13 }} \approx 0.555[/tex]
[tex]tan\angle X = \dfrac{Opposite \ leg \ length}{Adjacent\ leg \ length}[/tex]
The hypotenuse length = √(2² + 3²) = √13
Therefore;
[tex]\mathbf{tan( \theta)} = \dfrac{3 - 0}{2 - 0 } \mathbf{=\dfrac{3}{2 }}[/tex]
tan(θ) = 1.5
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Complete the Venn diagram.
in the junior side it is 22 the middle is 8 the girl side is 20 the outside is 16
Answer:
In sequence: 6, 8, 12 and 16
Step-by-step explanation:
Ok, the Venn diagram has 4 sections:
A - Juniors, but excluding girls (so boys only)
B - Juniors, who are also girls (so girls only)
C - Girls only, who aren't Juniors
D - Then outside the circles, for those who are not juniors and who are not girls (senior boys).
So, in A, you place the junior boys (6)
in B, you place the junior girls (8)
in C, you place the senior girls (12)
and in D, you place the senior boys (16)
The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm. Find the length of a diameter of the circle circumscribed about this triangle.
ANSWER
The length of a Diameter is 3.714
EXPLANATION
The circumscribed triangle is shown in the attachment.
We use the cosine ratio to find the altitude of the isosceles triangle.
[tex] \cos(60 \degree) = \frac{altitude}{hypotenuse} [/tex]
[tex] \cos(60 \degree) = \frac{altitude}{8} [/tex]
Altitude =8cos(60°)
Altitude=4cm
Let the upper half of the altitude be y cm.
Then the radius of the circle is (y-4)cm
The upper radius meets the tangent at right angles.
From the smaller right triangle,
[tex] \sin(60 \degree) = \frac{4 - y}{y} [/tex]
[tex] y\sin(60 \degree) = 4 - y[/tex]
[tex]y\sin(60 \degree) + y= 4 [/tex]
[tex](\sin(60 \degree) + 1)y= 4 [/tex]
[tex]y= \frac{4}{\sin(60 \degree) + 1} [/tex]
[tex]y = 16 - 8 \sqrt{3} [/tex]
y=1.857
The diameter is 2y
[tex]d = 32 - 16 \sqrt{3} [/tex]
=2(1.875)
The length of a Diameter is 3.714
Answer:
Diameter of the circle is 16 cm.
Step-by-step explanation:
Given : The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm.
To find : The length of a diameter of the circle circumscribed about this triangle?
Solution :
We construct a circle in which an ABC isosceles triangle is formed.
Refer the attached figure below.
The measure of a vertex angle of an isosceles triangle is 120° .
The length of a leg is 8 cm, AC=8 cm
Vertex angle is divided by the line touching the center of the circle.
So, [tex]\angle A=60^\circ[/tex] and line AD=radius of the circle
Applying property of isosceles triangle,
Now, ∠DAC=∠ACD=∠CDA=60°
AC=DC=8 cm
The radius of the circle is 8 cm.
The diameter of the circle is twice the radius.
Therefore, The diameter of the circle is d=2(8)=16 cm.