ANSWER:
[tex]t\leq7[/tex]EXPLANATION:
Given:
Melissa wants to rent a boat and spend at most $38
Cost of boat per hour = $6
Discount coupon off = $4
Let t represent the number of hours
We can go ahead and set up the below inequality;
[tex]6t-4\leq38[/tex]Let's add 4 to both sides of the inequality;
[tex]\begin{gathered} 6t-4+4\leq38+4 \\ 6t\leq42 \end{gathered}[/tex]Let's divide both sides by 6;
[tex]\begin{gathered} \frac{6t}{6}\leq\frac{42}{6} \\ t\leq6 \end{gathered}[/tex]So Melissa can rent the boat for up to 7 hours
The figure below shows a striaght line AB intersected by another straight line t: Write a paragraph to prove that the measure of angle 1 is equal to the measure of angle 3. (10 points)
Angles 1 and 3 are vertical angles, that is, are pairs of opposite angles made by intersecting lines. If 2 angles are vertical then they are congruent, in other words, they have the same measure.
15. When x =9, which number is closest to the value of y on the line of best fit in the graph below? 121917
We have a scatter plot.
We have to find the closest value to y on the line of best fit when x = 9.
We can estimate a line of best fit by hand in the graph as:
Although we have a data point where x = 9 and y =9, the line of best fit is kind of in between the two groups of points.
When we draw the line like this, the estimated value from the line of best fit when x = 9 is y = 12, as we can see in the graph.
Answer: 12
Can someone help me with this math question?
pic of question below
The Cartesian equation of the polar equation r² = 5 represents a circle centered at the origin and with radius √5.
What is the Cartesian form of a polar equation?
In this problem we find a polar equation, that is, f(r, θ) = C, whose Cartesian form must be found by using the following substitutions:
x² + y² = r² (1)
x = r · cos θ (2)
y = r · sin θ (3)
Then, the Cartesian form of r² = 5 is:
x² + r² = 5
The polar equation represents a circle centered at the origin and with a radius of √5.
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The Cartesian equation of the polar equation r² = 5 represents a circle centered at the origin and with radius √5.
What is Coordinate System?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points.
Given that r²=5
we find a polar equation,
x²+y²=r²
whose Cartesian form is found by substituting
x=rcosθ
y=rsinθ
as r²=5 then r=√5
So x²+y²=5.
This is equation of circle in polar form.
Hence it represents a circle with a radius of √5.
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Solve the system of two linear inequalities graphically. Graph the solution set of the first linear inequality? Type of boundary line? Two points on boundary line? Region to be shaded?
Answer:
Explanation:
Given the below system of linear inequality;
[tex]\begin{gathered} y<3 \\ y\ge-5 \end{gathered}[/tex]The graph of the linear inequality y < 3 will be a graph with a dashed line with a y-intercept of 3 since the inequality is not with an equal sign as seen below;
The graph of the 2nd linear inequality y >= -5 will be a graph with a solid line with a y-intercept of -5 since it has both the inequality sign and an equality sign as seen below;
Find the area of the shaded part of the figure if a=6, b=7, c=4. (I need help on this)
To obtain the area(A) of the shaded part of the figure, we will sum up the area of the triangle and the area of the rectangle.
Let us solve the area of the triangle(A1) first,
The formula for the area of the triangle is,
[tex]A_1=\frac{1}{2}\times base\times\text{height}[/tex]where,
[tex]\begin{gathered} base=b=7 \\ height=a=6 \end{gathered}[/tex]Therefore,
[tex]A_1=\frac{1}{2}\times7\times6=21unit^2[/tex]Hence, the area of the triangle is 21 unit².
Let us now solve for the area of the rectangle(A2)
The formula for the area of the rectangle is
[tex]A_2=\text{length}\times width[/tex]Where,
[tex]\begin{gathered} \text{length}=b=7 \\ \text{width}=c=4 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} A_2=7\times4=28 \\ \therefore A_2=28\text{unit}^2 \end{gathered}[/tex]Hence, the area of the rectangle is 28unit².
Finally, the total area of the shaded area is
[tex]\begin{gathered} A=A_1+A_2=21+28=49 \\ \therefore A=49unit^2 \end{gathered}[/tex]Hence, the area of the shaded part is 49unit² (OPTION A).
64 is 2/3percent of what number
We have to find the number x for which 64 is the 2/3.
The width of a 2-by-4 piece of wood is actually 34 inches. Find the total width of 28 2-by-4s laid side-by-side. Simplify youranswer.o 126 inchesO 98 inches0784 inches844 inches
The of one 2-by-4 piece of wood is 3.5 inches
To find the width of 28 pcs of wood, just multiply the number of wood to the actual width which is 3.5 inches
So we have :
[tex]28\times3.5=98[/tex]The answer is 98 inches
Suppose that the functions and g are defined for all real numbers x as follows. f(x) = x + 3; g(x) = 2x - 2 Write the expressions for (fg)(x) and (f - g)(x) and evaluate (f + g)(3)
Solution
Given
[tex]\begin{gathered} f(x)=x+3 \\ \\ g(x)=2x-2 \end{gathered}[/tex]Then
[tex](f\cdot g)(x)=f(x)\cdot g(x)=(x+3)(2x-2)=2x^2+4x-6[/tex][tex](f-g)(x)=f(x)-g(x)=(x+3)-(2x-2)=x-2x+3+2=5-x[/tex][tex](f+g)(3)=f(3)+g(3)=(3+3)+(2(3)-2)=6+4=10[/tex]Find the sin t as a fraction in simplest terms
We are asked to determine the sinT. To do that let's remember that the function sine is defined as:
[tex]\sin x=\frac{opposite}{hypotenuse}[/tex]In this case, we have:
[tex]\sin T=\frac{VU}{VT}[/tex]To determine the value of VU we can use the Pythagorean theorem which in this case would be:
[tex]VT^2=VU^2+TU^2[/tex]Now we solve for VU first by subtracting TU squared from both sides:
[tex]VT^2-TU^2=VU^2[/tex]Now we take the square root to both sides:
[tex]\sqrt[]{VT^2-TU^2^{}}=VU[/tex]Now we plug in the values:
[tex]\sqrt[]{(6)^2+(\sqrt[]{36^{}})^2}=VU[/tex]Solving the squares:
[tex]\sqrt[]{36+36}=VU[/tex]Adding the values:
[tex]\sqrt[]{2(36)}=VU[/tex]Now we separate the square root:
[tex]\sqrt[]{2}\sqrt[]{36}=VU[/tex]Solving the square root:
[tex]6\sqrt[]{2}=VU[/tex]Now we plug in the values in the expression for sinT:
[tex]\sin T=\frac{6\sqrt[]{2}}{6}[/tex]Now we simplify by canceling out the 6:
[tex]\sin T=\sqrt[]{2}[/tex]And thus we obtained the expression for sinT.
Gretchen is planting a rectangular garden. she wants to use 9 square feet for tulips.if garden has length of 8 feet by 3 feet, how much room will she have left for rest of her flowers
Given: the garden has a shape of a rectangle
The garden has a length of 8 feet by 3 feet
So, the area of the garden =
[tex]8\cdot3=24ft^2[/tex]she wants to use 9 square feet for tulips.
So, the remaining for rest of her flowers = 24 - 9 = 15 square feet
Each of the letters a through H has one of the 8 values listed. no 2 letters have the same value. The Simple arithmetic problems are clues for determining the value of each letter. Simply guess and check to find the values for letters a through H. You must use numbers listed below.
We have the following:
Let's start from the number C, which has two numbers that when adding it gives a number and subtracting two other numbers gives the same number C
C = 9, therefore:
[tex]\begin{gathered} F-D=9 \\ F=14 \\ D=5 \\ G+B=9 \\ G=3 \\ B=6 \\ 5+E=6\Rightarrow E=1 \\ 6+H=14\Rightarrow H=8 \\ A-9=8\Rightarrow A=17 \end{gathered}[/tex]What is the value of 0 put a comma and space between answer sin61°=cos=0; cos17°=sin0;
For
[tex]\begin{gathered} \sin 61=\cos \theta \\ \theta=\cos ^{-1}(\sin 61) \\ \end{gathered}[/tex]For
[tex]\begin{gathered} \cos 17=\sin \theta \\ \theta=\sin ^{-1}(\cos 17) \\ \end{gathered}[/tex]20 quarts=_ 20_×(1 quart) =_20_×(1\4 gallon) =_20/4_gallons =_5_gallons
From the question, we are to convert 20 quartz to gallons.
Given
1 quartz = 1/4 gallons
20 quartz = x
Cross multiply and find x;
1 * x = 20 * 1/4
x = 20/4
x = 5
Hence 20 quartz is equivalent to 5 gallons
A population of bacteria grows according to function p(t) = p. 1.42^t, where t is measured in hours. If the initial population size was1,000 cells, approximately how long will it take the population to exceed 10,000 cells? Round your answer to the nearest tenth.
Given the function p(t) and the initial condition, we have the following:
[tex]\begin{gathered} p(t)=p_0\cdot1.42^t \\ p(0)=1000 \\ \Rightarrow p(0)=p_0\cdot1.42^0=1000 \\ \Rightarrow p_0\cdot1=1000 \\ p_0=1000 \end{gathered}[/tex]Therefore, the function p(t) is defined like this:
[tex]p(t)=1000\cdot1.42^t[/tex]Now, since we want to know the time it will take the population to exceed 10,000 cells, we have to solve for t using this information like this:
[tex]\begin{gathered} p(t)=1000\cdot1.42^t=10000 \\ \Rightarrow1.42^t=\frac{10000}{1000}=10 \\ \Rightarrow1.42^t=10 \end{gathered}[/tex]Applying natural logarithm in both sides of the equation we get:
[tex]\begin{gathered} 1.42^t=10 \\ \Rightarrow\ln (1.42^t)=\ln (10) \\ \Rightarrow t\cdot\ln (1.42)=\ln (10) \\ \Rightarrow t=\frac{ln(10)}{\ln (1.42)}=6.56 \end{gathered}[/tex]Therefore, it will take the population 6.56 hours to exceed 10,000 cells
Find the radius of a circle in which a 24 cm chord is 4 cm closer to the center than a 16 cm chord. Round your answer to the nearest tenth.
The diagram representing the scenario is shown below
A represents the center of the circle. It divided each chord equally. Thus, we have CB = 16/2 = 8 for the shorter chord and DE = 24/2 = 12 for the longer chord
Assuming the distance between the
A
A landscaper has built a U-shaped raised bed in a vegetable garden as shown in the figure. How many cubic yards of soil should be ordered to fill the bed to a depth of 30 inches?
First calculate the area of the shaded region by considering the U-shaped bed as formed by three rectangles, as follow:
where the lengths of the sides of the rectangles corresponds with the dimensions of the U-shaped bed.
Then, for the area of the figure, use the formula for the area of a rectangle, for all three rectangles, as follow:
A = 5*18 + 3*20 + 5*18
A = 90 + 60 + 90
A = 240
Then, the area is 240 in^2
Next, convert the previous result to yd^2. Use the equivalence 1 yd = 36 in:
[tex]240in^2\cdot\frac{(1yd)^2}{(36in)^2}=0.185yd^2[/tex]Now, to find the volume convert 30 in to yards:
[tex]30in\cdot\frac{1yd}{36in}=0.83yd[/tex]Finally, multiply the previous result by the area of the figure:
[tex]0.185yd^2\cdot0.83yd=0.154yd^3[/tex]The mean of a population is 100, with a standard deviation of 15. The mean of
a sample of size 100 was 95. Using an alpha of .01 and a two-tailed test, what do
you conclude?
O Accept the null hypothesis. The difference is not statistically significant.
Reject the null hypothesis. The difference is statistically significant.
Accept the null hypothesis. The difference is statistically significant.
Reject the null hypothesis. The difference is not statistically significant.
We conclude that Reject the null hypothesis. The difference is statistically significant.
Define integers.The symbol used to represent integers is the letter (Z). A positive integer can be 0 or a positive or negative number up to negative infinity. The three elements that make up an integer are zero, the natural numbers, and their additive inverse. It can be shown on a number line, but without the fractional portion. Z stands for it.
A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043
Given,
The mean of a population is 100, with a standard deviation of 15. The mean of a sample of size 100 was 95.
z = [tex]\frac{95-100}{15/10}[/tex]
z = 3.333
Using the p value technique, the value of p is 0.0009, and since p = 0.0009 0.01 the null hypothesis is rejected, the conclusion is made.
Reject the null hypothesis. The difference is statistically significant.
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use the information provided to write the equation of each circle. center: (12,-13)point on circle: (18, -13)
Answer:
[tex](x-12)^2+(y+13)^2=36[/tex]Explanation:
Given:
• Center: (12,-13)
,• Point on circle: (18, -13)
First, we find the length of the radius.
[tex]\begin{gathered} r=\sqrt[]{(18-12)^2+(-13-(-13)_{})^2} \\ =\sqrt[]{(6)^2} \\ r=6\text{ units} \end{gathered}[/tex]The general equation of a circle is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Substituting the centre, (h,k)=(12,-13) and r=6, we have:
[tex]\begin{gathered} (x-12)^2+(y-(-13))^2=6^2 \\ (x-12)^2+(y+13)^2=36 \end{gathered}[/tex]The equation of the circle is:
[tex](x-12)^2+(y+13)^2=36[/tex]1. On Monday, Mike's account balance shows $-135, on Tuesday, Mikequickly deposited $200. What is his new balance on Tuesday? Write anequation for the situation and find the answer. *
Ok we need to write an equation for the situation and find the answer. So, let's do it:
Balance on tuesday=previus balance+deposit
Replacing we get:
Balance on tuesday=-135+200=$65
The new balance on tuesday is $65.
solve the proportion 4/3 is equal to 9 / X
We need to solve for X.
The proportion is:
[tex]\frac{4}{3}=\frac{9}{X}[/tex]To solve for X, we cross multiply and then use algebra to solve. The process is shown below:
[tex]\begin{gathered} \frac{4}{3}=\frac{9}{X} \\ 4\times X=3\times9 \\ 4X=27 \\ X=\frac{27}{4} \end{gathered}[/tex]determine the volume of each rectangular or triangular prism round to the nearest tenth if necessary
Determine the volume of each rectangular or triangular prism round to the nearest tenth if necessary
____________________
volume = base (B)* height (H)
_____________________
Base area
Triangle
B = b*h/2
Rectangle
B= L1*L2
__________________
volume = base (B)* height (H)
H= 15
Triangle case
B = 4.8 *9.6 /2
B = 46.08 / 2
B= 23.04
V= 23. 04* 15
V= 345.6 in ^3
Graph the following inequality.Note: To graph the inequality:Select the type of line below (solid or dashed).Plot two points on the line.Click on the side that should be shaded.
Given:
[tex]-4x-y>2[/tex]Consider the line,
[tex]-4x-y=2[/tex]Find the points on the line,
[tex]\begin{gathered} x=0 \\ -4(0)-y=2\Rightarrow y=-2 \\ x=1 \\ -4(1)-y=2\Rightarrow y=-6 \\ x=-1 \\ -4(-1)-y=2\Rightarrow y=2 \end{gathered}[/tex]The graph of the line is,
Now, find the region for inequality.
Consider any point from the right and the left side of the line and check which side satisfies the inequality.
[tex]\begin{gathered} R=(2,0) \\ -4x-y>2 \\ -4(2)-0=-8\text{ >2 is not true.} \end{gathered}[/tex]And,
[tex]\begin{gathered} L=(-2,0) \\ -4x-y>2 \\ -4(-2)-0=8>2\text{ is true} \end{gathered}[/tex]Therefore, the graph of the inequality is,
Note that inequality does not contain boundary points.
Find y if the line through (5, 1) and (6, y) has a slope of 3.
Answer:
Y = 32
Step-by-step explanation:
Y = mx + c, with a slope of 3
Y = 3x + c
Substitute values:
1 = 3 (5) + c
1 = 15 + c
c = -14
Rewrite formula:
Y = 3x - 14
Y = 3 (6) + 14
Y = 18 + 14
Y = 32
Hope this helps :)
Answer:
y = 4
Step-by-step explanation:
y = mx + b is the slope intercept form of a line.
We need an m (slope and a b(y-intercept)
They give us the slope, so we have to find the b
slope = 3
y = 1
x = 5
We need and x and y on the line and the point (5,1) gives us that.
y = mx + b
1 = 3(5) + b
1 = 15 + b Subtract 15 from both sides of the equation
-14 = b
Now we have the m (slope of 3) and the b (the y-intercept of -14)
y = mx + b
y = 3x -14 Now plug is the x (6) from the point given and solve for its y
y = 3(6) -14
y = 18 - 14
y = 4
The selling price of a refrigerator, is $537.60. If the markup is 5% of the dealer's cost, what is the dealer's cost of the refrigerator?
The cost price of dealer is $512.
We have to find the dealer's cost of refrigerator.
We know that mark up is on dealer's cost.
We have been given the markup as 5%
Let the dealer's cost of refrigerator be x,
Now, we know that there is a markup on it
So, we will calculate the marked up price
Marked up price = (Cost price * Markup percent)/100 + cost price
Marked up price = x*5/100 + x
Marked up price = 5x/100 + x
Marked up price = x/20 + x = (x+20x)20
Marked up price = 21x/20
We know that marked up price is the selling price and we have been given the selling price of the refrigerator
537.60 = 21x/20
537.60*20 = 21x
10752 = 21x
x = 10752/21
x = 512
The dealer's cost price is $512.
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Review the proof. Which step contains an error? step 2 step 4step 6step 8
Answer
Option C is correct.
Step 6 contains the error.
Explanation
Looking through the steps, we can see easily that the mistake occurs at the 6th step, specifically when the process moves from step 5 to step 6
-1 + cos θ = -2 sin² (θ/2)
If one multiplies through by -1
1 - cos θ = 2 sin² (θ/2)
NOT 1 + cos θ = 2 sin² (θ/2)
Hope this Helps!!!
The radius of a circle is 6 kilometers. What is the area of a sector bounded by a 126° arc?Give the exact answer in simplest form. ____ square kilometers.
It is given that the radius is 6 kilometers and the arc is 126 degrees.
The area of sector is given by:
[tex]\frac{126}{360}\times\pi\times6^2=39.5840\operatorname{km}^2[/tex]Therefore the area is 39.5840 square kilometers.
If a car in 3 hours travels 156 miles, what is the speed of the car in miles per hour?
To calculate the speed a vehicle is traveling you have to use the following formula:
[tex]S=\frac{d}{t}[/tex]Where
S: speed
d: distance
t: time
The car traveled d=156miles in t=3hs
Its speed can be calculated as:
[tex]\begin{gathered} S=\frac{156}{3} \\ S=52 \end{gathered}[/tex]The car's speed was 52 miles per hour
In AOPQ, 0 = 500 cm, p = 600 cm and q=380 cm. Find the measure of P to thenearest 10th of a degree.
Answer: Triangle has three sides, which are:
[tex]\begin{gathered} O=500\operatorname{cm} \\ P=600\operatorname{cm} \\ Q=380\operatorname{cm} \\ \end{gathered}[/tex]We need to find the angle p, that is right across the side P:
[tex]\angle A=\arccos (\frac{b^2+c^2+a^2}{2bc})=0.97895\text{rad}=56.09\text{degres}[/tex]This is the value of angle A
At Paul's Pet Palace, 3/16 of the animals are dogs and 5/24 of the animals are cats. What fraction of the animals are neither dogs nor cat?
You have that 3/16 of the animals are dogs and 5/24 of the animals are cat.
To determine the fraction of animals that are neither dogs nor cat, consider the following:
If 3/16 are dogs, then 13/16 are other animals, but from this fraction, 5/24 are cats. Then, the subtraction 13/16 - 5/24 results in the fraction of animals that are neither dogs nor cat:
[tex]\frac{13}{16}-\frac{5}{24}=\frac{312-80}{384}=\frac{232}{384}[/tex]simplify the last fraction:
[tex]\frac{232}{384}=\frac{116}{192}=\frac{58}{96}=\frac{29}{48}[/tex]Hence, 29/48 of the animal are neither dogs nor cats
In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distances from 100 yards to 10 miles. His formula is given by t= 0.0588s^(1.125) where s is the distance in meters and t is the time to run thatdistance in seconds.a. Find Kennelly's estimate for the fastest a human could possibly run 1609 meters.t= seconds (Round to the nearest thousandth as needed.)
For this problem, we are given a formula that predicts the fastest a human can run a certain distance. We need to determine the time a human can run 1609 meters.
The formula is:
[tex]t=0.0588s^{1.125}[/tex]We need to replace s with 1609 and solve for t.
[tex]\begin{gathered} t=0.0588(1609)^{1.125}\\ \\ t=0.0588\cdot4049.26\\ \\ t=238.096 \end{gathered}[/tex]The fastest a human can run 1609 meters is 238.096 seconds.