Answer:
Y = 26
Step by step explanation:
[tex]y\text{ + 41 = 67}[/tex]
Then we pass the 41 to substract.
[tex]y\text{ = 67 - 41 = 26}[/tex]-ractions:
On a website, there is an ad for jeans every 5 minutes, an ad for sneakers
every 10 minutes, and an ad for scarves every 45 minutes.
If they all appeared together at 9:00 P.M., when is
the next time they will all appear together?
ICM to solve the problem
Answer:
Step-by-step explanation:
Function Notation - TransformationIll send a picture of the question
Given the vertices of the original quadilateral:
(3, 4), (5, 6), (7, 4), and (5, 3)
Vertices of the transformed quadilateral:
(-5, -6), (-3, -4), (-1, -6), and (-3, -7)
Let's describe the transformation rule used for this transformation.
To find the transformation rule, let's find the number of movements in the x-direction and y-direction that would map the original quadilateral to the transformed quadilateral by subtracting the x and y coordinates of the coresponding sides.
We have:
(x, y) ==> (-5 -3, -6 -4) ==> (-8, -10)
(x, y) ==> (-3 -5, -4, -6) ==> (-8, -10)
(x, y) ==> (-1 -7, -6 -4) ==> (-8, -10)
(x, y) ==> (-3 -5, -7 -3) ==> (-8, -10)
For all corresponding sides, we have: (x, y) ==> (-8, -10)
This means there was a shift 8 units to the left, and 10 units downwards.
Therefore, the rule for the transformation shown here is:
(x, y) ==> (x - 8, y - 10)
ANSWER:
B. f(x, y) = (x - 8, x- 10)
Which of the following is the number of sides a polygon can have to form aregular tessellation?O A. 9B. 3C. 5D.7
From the image, we are asked the number of sides a polygon can have to form a regular tesselation.
The first step is to understand what a regular tessellation is;
A regular tessellation is a highly symmetric, edge-to-edge tiling made up of regular polygons, all of the same shape. There are only three regular tessellations: those made up of equilateral triangles, squares, or regular hexagons.
This implies that it could either have 3 sides(triangle), four sides(square), six sides(hexagon).
From the given options we can clearly see that 3 sides is the only available option.
ANSWER: Option B
Which interval notation represents a function with a domain of all real numbers greater than or equal to 4?A.) -35 D.) y>0 E.) Y<4
If the domain is all real numbers greater than or equal to 4, the interval will be
[tex]x\ge4[/tex]Find percent change of 50 to 43
Answer:
-14.00%
Step-by-step explanation:
((43-50)/50)*100 = -14.00%
Find the cosine of angle R. Reduce the answer to the lowest terms.
Cosine formula
[tex]\cos (angle)=\frac{\text{ adjacent side}}{\text{ hypotenuse}}[/tex]Considering angle R, the adjacent side has a length of 9 units, and the hypotenuse of the triangle has a length of 15 units. Substituting this information into the above formula:
[tex]\cos (m\angle R)=\frac{9}{15}=\frac{\frac{9}{3}}{\frac{15}{3}}=\frac{3}{5}[/tex]This is Calculus 1 Problem! MUST SHOW ALL THE JUSTIFICATION!!!
Given: A surveyor standing 50 feet from the base of a large tree measures the angle of elevation to the top of the tree as 75.8 degrees.
Required: To determine how accurately the angle must be measured if the percent error in estimating the tree's height is less than 5%.
Explanation: To estimate the angle, we will use the trigonometric ratio
[tex]tanx=\frac{h}{50}\text{ ...\lparen1\rparen}[/tex]where h is the tree's height, and x is the angle of elevation to the top of the tree.
Hence we get
[tex]\begin{gathered} h=50\cdot(tan75.8\degree) \\ h=197.59\text{ feet} \end{gathered}[/tex]Now differentiating equation 1, we get
[tex]sec^2xdx=\frac{1}{50}dh[/tex]We can write the above equation as:
[tex]sec^2x\cdot\frac{xdx}{x}=\frac{h}{50}\cdot\frac{dh}{h}\text{ ...\lparen2\rparen}[/tex]Also, it is given that the error in estimating the tree's height is less than 5%.
So
[tex]\frac{dh}{h}=0.05[/tex]Also, we need to convert the angle x in radians:
[tex]x=1.32296\text{ rad}[/tex]Putting these values in equation (2) gives:
[tex]\frac{dx}{x}=\frac{197.59}{50}\cdot\frac{cos^2(1.32296)}{1.32296}\cdot0.05[/tex]Solving the above equation gives:
[tex]\begin{gathered} \frac{dx}{x}=3.9518\cdot0.04548551012\cdot0.05 \\ =0.008987\text{ radians} \end{gathered}[/tex]Let
[tex]d\theta\text{ be the error in estimating the angle.}[/tex]Then,
[tex]\lvert{d\theta}\rvert\leq0.008987\text{ radians}[/tex]Final Answer:
[tex]\lvert{d\theta}\rvert\leq0.008987\text{ radians}[/tex]How do I write down the size of Angles and marked by letters?
we can assume the lines are parallels so both triangles will have equal angles, so:
s=55° and p=x
now if we add 110 and x, we have a line this means
110+x=180
x=180-100
x=80
so p=x=80
and finally, the angles inside a triangle must add 180° so
55+p+t=180
55+80+t=180
135+t=180
t=180-135=45
So the answer is:
p=80°
s=55°
t=45°
PLEASE help I'll send a picture in later.
Given
Table of names
Procedure
Names end with an E
Gabe
Steve
The probability would be independent and equal to:
[tex]\begin{gathered} \frac{2}{6}\cdot\frac{2}{6} \\ \frac{4}{36} \\ \\ \frac{1}{9} \end{gathered}[/tex]The probability would be 1/9
I was doing this with a tutor but there was a connection problem.
ANSWER:
[tex](x-3)^2+(y+7)^2=113[/tex]The point (7,6) is not on the circle
STEP-BY-STEP EXPLANATION:
(a)
The equation of the circle is given as follows:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{ where (h,k) is the center and r is the radius } \end{gathered}[/tex]We replace to calculate the radius of the circle, like this:
[tex]\begin{gathered} \mleft(-4-3\mright)^2+\mleft(1-\mleft(-7\mright)\mright)^2=r^2 \\ (-7)^2+(8)^2=r^2 \\ r^2=113 \end{gathered}[/tex]Therefore, the equation would be:
[tex](x-3)^2+(y+7)^2=113[/tex](b)
We replace the point, and if the value is greater than the radius, it means that this point is not on the circle:
[tex]\begin{gathered} (x-3)^2+(y+7)^2\le113 \\ \text{ replacing:} \\ \mleft(7-3\mright)^2+\mleft(6+7\mright)^2\le113 \\ 4^2+13^2\le113 \\ 16+169\le113 \\ 185\le113 \end{gathered}[/tex]Therefore, the point (7,6) is not on the circle
14|x + 14| + 13 =-69
Solve for x
Answer: No real solutions
Step-by-step explanation:
[tex]14|x+14|+13=-69\\\\14|x+14|=-82\\\\|x+14|=-82/14[/tex]
Since absolute value is always non-negative, there are no real solutions.
Determine whether the graph shown is the graph of a polynomial function
the given graph is smooth and its domain is containing all real numbers
so it is a polynomial function.
Complete the description of the piece wise function graphed below
Analyze the different intervals at which the function takes the values provided by the graph. Pay special attention on the circles, whether they are filled up or not.
From the graph, notice that the function takes the value of 3 when x is equal to -4, -2 or any number between them. Therefore, the condition is:
[tex]f(x)=3\text{ if }-4\leq x\leq-2[/tex]If x is greater (but not equal) than -2 and lower or equal to 3, the function takes the value of 5. Therefore:
[tex]f(x)=5\text{ if }-2Notice that the first symbol used is "<" and the second is "≤ ".Finally, the function takes the value of -3 whenever x is greater (but not equal) to 3 and less than or equal to 5. Then:
[tex]f(x)=-3\text{ if }3In conclusion:[tex]f(x)=\mleft\{\begin{aligned}3\text{ if }-4\leq x\leq-2 \\ 5\text{ if }-2The total movie attendance in a country was 1.16 billion people in 1990 and 1.40 billion in 2008. Assume that the pattern in movie attendance is linear function of time. (Need to answer questions a-d for this question - pic attached)
a)
In order to find a function M(t), first let's identify two ordered pairs that are solutions to the equation.
From the given information, we have the ordered pairs (1990, 1.16) and (2008, 1.4).
Using these ordered pairs, let's find the slope-intercept form of a linear equation (y = mx + b)
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1.4-1.16}{2008-1990}=\frac{0.24}{18}=0.01333 \\ \\ y=mx+b \\ 1.16=1990\cdot0.01333+b \\ b=-25.3667 \\ \\ y=0.01333x-25.3667 \end{gathered}[/tex]So the equation is M = 0.01333t - 25.3667
The independent variable represents the year (correct option: first one)
b)
The slope represents the change in M over the change in t, that is, it represents the change in attendance over a year (correct option: first one)
c)
For t = 2015, we have:
[tex]\begin{gathered} M=0.01333\cdot2015-25.3667 \\ M=26.86-25.37 \\ M=1.49 \end{gathered}[/tex]d)
For M = 1.5, we have:
[tex]\begin{gathered} 1.5=0.01333\cdot t-25.3667 \\ 0.01333t=26.8667 \\ t=2015.5 \end{gathered}[/tex]Use the table to find the slope of the line.Round your answer out to two decimal places
Given:
The points are (8, -3) and (-5, 1).
To find the slope of the line:
The slope formula is,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{1-(-3)}{-5-8} \\ =\frac{1+3}{-13} \\ =-\frac{4}{13} \\ =-0.30769 \\ \approx-0.31 \end{gathered}[/tex]Hence, the slope of the line is -0.31 (rounded to the nearest two decimal places).
find the midpoint of PQ. P(6,4) and Q(4,3)
the midpoint between two points has the following formula
[tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]replace in the formula using P as point 1 and Q as point 2
[tex]\begin{gathered} (\frac{6+4}{2},\frac{4+3}{2}) \\ (\frac{10}{2},\frac{7}{2}) \\ (5,\frac{7}{2}) \\ (5,3.5) \end{gathered}[/tex]Please help!
How many solutions does the following equation have?
6 (c+4) = 6c + 30
zero solutions
one solution
infinitely many
solutions
The number of solutions that this equation have is: A. zero solutions.
What are zero solution?Generally speaking, an equation is said to have zero solution or no solution when the left hand side and right hand side of the equation are not the same or equal. This ultimately implies that, an equation would have zero solution or no solution when both sides of the equal sign are not the same and the variables cancel out.
How to determine the number of solutions?In order to determine the number of solutions that this equation have, we would simplify the equation by opening the bracket and then compare both sides of the equation as follows:
6(c+4) = 6c + 30
6c + 24 = 6c + 30
6c - 6c = 30 - 24
0 = 6 (no solution).
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The length of the diagonal of a Rectangle is 14cm,and it forms a 30 degree angle in one corner of the rectangle.What is the area of the rectangle.(A=LxW)Just number 20
Explanation
Step 1
draw the rectangle
here we have a rigth triangle,then
Let
[tex]\begin{gathered} hypotenuse=14 \\ agle=30\text{ \degree} \\ \text{adjacent side= length= l} \end{gathered}[/tex]so, we need a function that relates those values
[tex]\cos \Theta=\frac{adjacent\text{ side}}{\text{hypotenuse}}[/tex]replace and solve for length
[tex]\begin{gathered} \cos \Theta=\frac{adjacent\text{ side}}{\text{hypotenuse}} \\ \text{hypotenuse}\cdot\cos \Theta=adjacent\text{ side} \\ 14\text{ cm }\cdot\cos 30=l \\ 12.12435\text{ cm=l} \end{gathered}[/tex]Step 2
width
similarity, we need a function that relates
[tex]\sin \text{ }\Theta=\frac{opposite\text{ side}}{\text{hypotenuse}}[/tex]let
[tex]\text{opposite side= width=w}[/tex]replace and solve for w
[tex]\begin{gathered} \sin \text{ }\Theta=\frac{opposite\text{ side}}{\text{hypotenuse}} \\ \text{hypotenuse}\cdot\sin \Theta=opposite\text{ side} \\ 14\text{ cm }\cdot\sin \text{ 30=w} \\ 7cm=w \end{gathered}[/tex]Step 3
finally, the area of a rectangle is given by
[tex]\begin{gathered} \text{Area}=\text{ length }\cdot width \\ \text{replacing} \\ \text{Area}=(12.12\cdot7)(cm^2) \\ \text{Area}=84.87(cm^2) \end{gathered}[/tex]therefore, the answer is
[tex]\text{Area}=84.87(cm^2)[/tex]I hope this helps you
2. a) How many sets of opposite faces does this rectangular prism have? ____b) Why is the figure called a rectangular prism?
Answer:
a) 3 sets of opposite faces
b) The given figure is called a rectangular prism because its bases( the bottom face and the top face) are both rectangles.
Explanation:
a) Looking at the given rectangular prism and counting the faces, we can see that there are 6 faces in all. Out of the 6 faces of the rectangular prism, we can see that there are 3 pairs of opposite faces.
b) A prism is any 3-dimensional shape that has two identical shapes called bases facing each other.
If the two identical shapes facing each other are rectangles, then the prism is termed a rectangular prism.
Therefore, we can say that the given figure is called a rectangular prism because its bases ( the bottom face and the top face) are both rectangles.
J(-6-2)3-*NWMark this and return2--9-8-7-6-5-4-3-2-3₁ 1 2 3 4 5 61-5737-2-cd-6--7--8-2 do-9--10--11--12--13-8 9 10 11 xK(8,-9)What is the x-coordinate of the point that divides thedirected line segment from J to K into a ratio of 2:5?X == (m²²7 m )(x₂ − ×₁) + X₁m+n0 000-22Save and ExitNextSubmit
Use the given formula:
[tex]x=(\frac{m}{m+n})(x_2-x_1)+x_1[/tex]Being m: 2 and n: 5
x1: -6
x2: 8
[tex]\begin{gathered} x=(\frac{2}{2+5})(8-(-6))+(-6) \\ \\ x=\frac{2}{7}*(14)-6 \\ \\ x=4-6 \\ \\ x=-2 \end{gathered}[/tex]Then, the x-coordinate of th point that divides the directed line segment from J to K into a ratio 2:5 is -2Answer: -20 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 10401234 5 6 7 8 9 10OB.C.OD. +Reset Selection
Okay, here we have this:
Considering the provided inequation, we are going to identify how can be represented on a number line, so we obtain the following:
So the first thing we will do is factor to find the solution intervals, we have:
[tex]\begin{gathered} 3x^2-27x\leq0 \\ x(x-9)\leq0 \\ 0\leq x\leq9 \end{gathered}[/tex]According to this, we finally obtain that the solution interval is option D, because it satisfies the found interval and its endpoints are closed.
Choose the correctdomain for thequadratic function.А-00 > X < 0B-00 < x < 0
The function given in the graph stretches from negative to positive infinity.
Hence the domain of the function is given by:
[tex]-\inftyOption B is correct.fredrico has earned scores of 7.2, 8.4, and 8.4 on his first 3 dives he has one dive left what score must he get on his last dive to have an average of at least 7.4 on all four dives
For Fredrico to make an average of at least 7.4 on all four dives, he must get at least 5.6 in his last dive.
What is the average?The average is the mean of the total scores that Fredrico scored in his dives.
The average can be computed by dividing the total scores by the number of dives.
The average is the quotient of the division operation of the total scores and the number of dives.
The total score based on an average of 7.4 = 29.6
The total scores obtained = 24 (7.2 + 8.4 + 8.4)
The remaining score to obtain to get the average of 7.4 = 5.6 (29.6 - 24)
Thus, Fredrico needs an additional 5.6 score in the last dive to make the average.
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Fredrico needs to score at least 5.6 on his final dive in order to achieve an average of at least 7.4 on all four dives.
Let's assume the required score would be x on his final dive
Mean = ∑x/n
The average represents the mean of all of Fredrico's dive-related scores.
Here, n = 4
Sum of Observations (∑x) = 7.2 + 8.4 + 8.4 + x
∑x = x + 24
Mean = ∑x/n
Substitute the values in the above formula,
⇒ 7.4 = (x + 24) / 4
Apply the cross-multiplication operation in the above equation,
⇒ 7.4 × 4= (x + 24)
⇒ 29.6 = x + 24
⇒ x = 29.6 - 24
Apply the subtraction operation to get
⇒ x = 5.4
Therefore, Fredrico needs to score at least 5.6 on his final dive
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In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to
a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability that a female will be born using this technique is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
Does the technique appear effective in improving the likelihood of having a female baby?
O No
The probability of being a girl child to a couple is 0.9498
Yes, this technique appear effective in improving the likelihood of having a female baby
Given,
In a sex selection technique,
The number of female babies in the result = 284
The number of male babies in the result = 15
Total children = 284 + 15 = 299
We have to find the probability of being a girl child;
Probability;
Probability refers to potential. Probability values are limited to the range of 0 to 1. Its fundamental notion is that something is probable to occur. It is the proportion of favorable events to all other events.
Here,
The probability of being a girl child, P = 284/299 = 0.9498
That is,
The probability of being a girl child to a couple is 0.9498
Yes, this technique appear effective in improving the likelihood of having a female baby
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A periodic deposit is made into an annuity with the given terms. Find how much the annuity will hold at the end of the specified amount of time. Round your answer to the nearest dollar.Regular deposit:$1300Interest rate:4.2%FrequencyannuallyTime:17 yearsFuture value: $
SOLUTION
We will use the formula
[tex]FV=P\lbrack\frac{(1+r)^n-1}{r}\rbrack[/tex]Where FV represents the future value annuity
P = Periodic payment = 1300
r = interest rate = 4.2% = 0.042
n = number of periods = 17 years.
So we have
[tex]\begin{gathered} FV=P\lbrack\frac{(1+r)^n-1}{r}\rbrack \\ FV=1300\lbrack\frac{(1+0.042)^{17}-1}{0.042}\rbrack \\ FV=1300\lbrack\frac{(1.042)^{17}-1}{0.042}\rbrack \\ FV=31,341.485 \end{gathered}[/tex]Hence, the answer becomes $31,341 to the nearest dollar
In the triangle below, suppose that mZH= (6x-4)°, mZ1 = (2x-5)°, and m
Find the degree measure of each angle in the triangle.
(2x - 5) ⁰
H (6x-4)
x
mZH =
m 41 =
mZJ =
1
X
Answer: H = 122, I = 37, J = 21
Step-by-step explanation:
All the angles of a triangle add up to 180 degrees.
(6x - 4) + (2x - 5) + x = 180
Combine like terms
9x - 9 = 180
Solve for x
9x = 189
x = 21
m<H = (6*21 - 4) = 122
m<I = (2*21-5) = 37
m<J = 21
Find the lateral area of the cylinder .The lateral area of the given cylinder is _ M2(Round to the nearest whole number as needed .)
The lateral area of a cylinder is:
[tex]LA=2\pi rh[/tex]r is the radius
h is the height
For the given cylinder:
As the diameter is 4m, the radius is half of the diameter:
[tex]r=\frac{4m}{2}=2m[/tex]h=12m
[tex]\begin{gathered} SA=2\pi(2m)(12m) \\ SA=48\pi m^2 \\ SA\approx151m^2 \end{gathered}[/tex]Then, the lateral area of the given cylinder is 151 square metersYou want to build a sandbox that can hold50,445 cubic inches of sand. If the sandbox is to be59 in. long and57 in. wide, how tall will it need to be?
Volume of sandbox (to be built) = 50,445 cubic inches
A sandbox is the shape of a cuboid and is calculated by the formula
[tex]\text{volume = length }\cdot\text{ wi}\differentialD tth\text{ }\cdot\text{ height }\Rightarrow\text{ v = l }\cdot\text{ w }\cdot\text{ h}[/tex]Volume = Length * Width * Height
Volume = 50,445 cubic inches, Length = 59 in. Width = 57 in, Height = ?
50,445 = 59 * 57 * h
Make h the subject of the formula, we have:
h = 50445 / (59 * 57) = 15 in
Form a polynomial whose zeros and degree are given.Zeros: -4, multiplicity 2; -3, multiplicity 1; degree 3O x3 + 8x2 + 40x + 48O x3 - 11x2 + 24x - 48O x3 + 11x2 + 40x + 48O x3 - 11x2 + 40% - 48
the city pays students $50 per day to serve snow cones at the local summer festival. Analyze the potential earnings of a student who works the whole week of the festival if working partial days is not permitted. this situation can be modeled by the function f(x)=50x.What is a reasonable maximum value for the dependent variable? Explain how you arrived at your answer.
Given:
The per day earning $50
The function is
[tex]f(x)=50x[/tex]Find-:
The maximum value of earning
Explanation-:
The function is
[tex]f(x)=50x[/tex]Where,
[tex]x=\text{ Number of days}[/tex]The students work for a whole week.
[tex]1\text{ week }=7\text{ Days}[/tex]So the maximum value is
[tex]\begin{gathered} f(x)=50x \\ \\ x=7 \\ \\ f(7)=50\times7 \\ \\ f(7)=350 \end{gathered}[/tex]The maximum earning is $350
