Both the decorative light strands will change change the colors at the same time again after 448 seconds
In the above question, it is given that,
Two strands of decorative lights, red and blue is one strand and green and yellow is another are hanged
Strand one changes colors in = 16 seconds
Strand two changes colors in = 28 seconds
We need to find, after how many seconds will the strands change color at the same time again
To find this, we will take the LCM(Lowest Common Multiple) of both strands time
Factors of 16 = 2 x 2 x 2 x 2
Factors of 28 = 2 x 2 x 7
LCM( 16 and 28) = 2 x 2 x 2 x 2 x 2 x 2 x 7 = 448
Therefore, It can be concluded that, both the decorative light strands will change change the colors at the same time again after 448 seconds
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What would be equivalent to 11 to the power of 8 over 11 to the power of 3
Given
[tex]\frac{11^8}{11^3}[/tex]To find the equivalent expression.
Explanation:
It is given that,
[tex]\frac{11^8}{11^3}[/tex]That implies,
[tex]\begin{gathered} \frac{11^8}{11^3}=11^{8-3} \\ =11^5 \\ =11^{1+4} \\ =11\times11^4 \end{gathered}[/tex]Hence, the answer is 11×11⁴.
The point A(4, 1) is reflected over the point (0, -3) and its image is point B. What are the coordinates of point B?
A reflection over the point (0,0) is given by:
[tex](x,y)\rightarrow(-x,-y)[/tex]Nevertheless, the reflection is being made over the point (0,-3). We can first make a traslation of the point (0,-3) to the origin. Then, reflect the new coordinates of the point A through the origin and then bring back the new origin to (0,-3).
First, make a traslation such that the new coordinates of (0,-3) are (0,0):
[tex](x,y)\rightarrow(x,y+3)[/tex]Then, apply a reflection through the origin:
[tex](x,y+3)\rightarrow(-x,-y-3)[/tex]Finally, make a traslation reciprocal to the first one:
[tex](-x,-y-3)\rightarrow(-x,-y-3-3)=(-x,-y-6)[/tex]Therefore, the reflection over the point (0,-3) can be written as:
[tex](x,y)\rightarrow(-x,-y-6)[/tex]Substitute (x,y)=(4,1) to find out the new coordinates of A after the reflection:
[tex]\begin{gathered} A\rightarrow B \\ \Rightarrow(4,1)\rightarrow(-4,-1-6)=(-4,-7) \end{gathered}[/tex]Therefore, the coordinates of the point B are (-4,-7).
A triangle is shown.Drag graphs to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, or the line =y=x.
ANSWER:
STEP-BY-STEP EXPLANATION:
The first thing is to establish the points of which the triangle forms.
Now we apply the rule of reflection in each case.
1. x -axis
[tex]P(x,y)\rightarrow P^{\prime}(x,-y)[/tex]In this case:
[tex]\begin{gathered} A(1,-3)\rightarrow A^{\prime}(1,3) \\ B(3,-2)\rightarrow B^{\prime}(3,2) \\ C(4,-5)\rightarrow C^{\prime}(4,5) \end{gathered}[/tex]Therefore, the x-axis image is:
2. y-axis
[tex]P(x,y)\rightarrow P^{\prime}(-x,y)[/tex]In this case:
[tex]\begin{gathered} A(1,-3)\rightarrow A^{\prime}(-1,-3) \\ B(3,-2)\rightarrow B^{\prime}(-3,-2) \\ C(4,-5)\rightarrow C^{\prime}(-4,-5) \end{gathered}[/tex]3. y = x
[tex]P(x,y)=P^{\prime}(y,x)[/tex]In this case:
[tex]\begin{gathered} A(1,-3)\rightarrow A^{\prime}(-3,1) \\ B(3,-2)\rightarrow B^{\prime}(-2,3) \\ C(4,-5)\rightarrow C^{\prime}(-5,4) \end{gathered}[/tex]Match the inequality to its graph. -2y > 2
The solution is presented in the form of four figures labeled with inequality.
What is meant by inequality?The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It's an example of inequity. This means that the left part, 5x 4, is greater than the right part, 2x + 3. We'll be looking for x values for which the inequality holds true. The term inequality refers to a mathematical expression in which the sides are not equal. An inequality compares any two values and shows that one is less, greater, or equal to the value on the other side of the equation.Given inequality are
A) 2x > (-6)
B) 6 + x ≤ 3
C) x - 4 < (-7)
D) -x - 5 ≤ (-2)
Simplifying the graph for matching with givens...
A) 2x > (-6)
Divide 2 on both sides
x>(-3)
B) 6 + x ≤ 3
Add (-6) on both side.
[tex]&6+x+(-6) \leq 3+(-6) \\[/tex]
[tex]&x \leq(-3)[/tex]
C) x - 4 < (-7)
Add (4) on both side.
[tex]&x-4+4 < (-7)+4 \\[/tex]
[tex]&x < (-3)[/tex]
D) -x - 5 ≤ (-2)
Multiple (-1) on both side
[tex]+x+5 \geq(+2)[/tex]
Note: The sign of the inequality changes due to the multiplication of a negative number Add (-5) on both sides.
x ≥ (-3)
The complete question is:
Match the inequality with its line graph.
A) 2 x > -6
B) 6 + x ≤ 3
C) x - 4 < -7
D) - x - 5 ≤ -2
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The radius r of a sphere is increasing at a rate of 4 inches per minute. Find the rate of change of the volume when r =2 inches
Given the word problem, we can deduce the following information:
1. The radius r of a sphere is increasing at a rate of 4 inches per minute.
2. r =2 inches
To determine the change in volume, we first use the formula of the volume of sphere:
[tex]V=\frac{4}{3}\pi r^3[/tex]where:
V=Volume
r=radius
Next, we take the derivative of the volume:
[tex]\begin{gathered} V=\frac{4}{3}\pi r^{3} \\ \frac{dV}{dt}=\frac{4}{3}\frac{\pi3r^2dr}{dt} \\ Simplify \\ \frac{dV}{dt}=4\pi r^2\cdot\frac{dr}{dt} \\ \end{gathered}[/tex]Hence,
[tex]\frac{dr}{dt}=4\frac{\text{ inches}}{minute}[/tex][tex]r=2\text{ inches}[/tex]We plug in r=2 and dr/dt=4 into the derivative of the volume of sphere:
[tex]\begin{gathered} \frac{dV}{dt}=4\pi r^{2}\frac{dr}{dt} \\ \frac{dV}{dt}=4\pi(2)^2(4) \\ Calculate \\ \frac{dV}{dt}=201.06\text{ }\frac{in^3}{minute} \end{gathered}[/tex]Therefore, the rate of change of the volume is 201.06 in^3/min.
I'll send you a pic of the equation
g(h(0)):
[tex]\begin{gathered} g\lbrack h(x)\rbrack=(x^2-1)+4 \\ g\lbrack h(0)\rbrack=0^2-1+4 \\ g\lbrack h(0)\rbrack=3 \end{gathered}[/tex]answer: g[h(0)]=3
What is the angle between vectors u = <5, -2, 4> and v=<4, 6, 2> ? (rounded to the nearest degree)1º359°10°71°
The formula is;
[tex]\begin{gathered} u.v=\lvert{u\lvert{}\rvert v}\rvert cos\theta \\ \end{gathered}[/tex][tex]\begin{gathered} u.v=5(4)+(-2)(6)+4(2) \\ u.v=16 \end{gathered}[/tex][tex]\begin{gathered} \lvert{u}\rvert=\sqrt{(5^2+-2^2+4^2)}\text{ } \\ \lvert{u=\sqrt{45}}\rvert \end{gathered}[/tex][tex]\begin{gathered} \lvert{v}\rvert=\sqrt{4^2+6^2+2^2} \\ \lvert{v}\rvert=\sqrt{56} \end{gathered}[/tex][tex]16=\sqrt{45}X\sqrt{56}\text{ }cos\theta\text{ }[/tex][tex]\cos\theta=\frac{16}{\sqrt{45}X\sqrt{56}}=\frac{16}{50.1996}=0.3187[/tex][tex]\theta=\cos^{-1}(0.3187)=\text{ 71}\degree[/tex]θ = 71°
3) Billy's Restaurant ordered 210 flowers for Mother's Day. They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each. They ordered mostly carnations, and 20 fewer daisies than roses. The total order came to $667.50. How many of each type of flower was ordered?
Total number of flowers = 210
Carnations = c = $1.50
Roses = r = $5.75
Daisies = d = $2.60
d = r - 20
Total price = $667.5
Equation 1
1.5c + 5.75r + 2.6d = 667.5
Equation 2
c + r + d = 210
Equation 3
d = r - 20
Solve by substitution
1.5c + 5.75r + 2.6(r - 20) = 667.5
1.5c + 5.75r + 2.6r - 52 = 667.5
1.5c + 8.35r = 667.5 + 52
1.5c + 8.35r = 719.5
c + r + r - 20 = 210
c + 2r = 210 + 20
c + 2r = 230
Solve for c
x c = 230 - 2r
1.5(230 - 2r) + 8.35r = 719.5
345 - 3r + 8.35r = 719.5
5.35r = 719.5 - 345
5.35r = 374.5
r = 374.5/5.35
r = 70
e c = 230 - 2(70)
c = 230 - 140
c = 90
d = 70 - 20
d = 50
Billy ordered 70 roses, 90 carnations and 50 daisies.
5
345 - 3r + 8.35r = 719.5
5.35r = 719.5 - 345
5.35r = 374.5
r = 374.5/5.35
r = 70
e c = 230 - 2(70)
c = 230 - 140
c = 90
d = 70 - 20
d = 50
Billy ordered 70 roses, 90 carnations and 50 daisies.
You multiply a number by 3 subtract 6 then add 2 the results is 20 what's the number
You multiply a number by 3 subtract 6 then add 2 the results is 20
what's the number ?
Let the number = x
multiply a number by 3
so, it becomes 3x
subtract 6 , so, 3x - 6
then add 2
so, 3x - 6 + 2
The result will be 20
So,
3x - 6 + 2 = 20
solve for x
3x - 4 = 20
Add 4 to both sides
3x - 4 + 4 = 20 + 4
3x = 24
Divide both sides by 3
3x/3 = 24/3
So,
x = 8
4. Name the quadrant in which point (4,1) is located.a. IIb. Ic. IIId. IV
A Coordinate plane has two perpendicular number lines. The vertical line is the y-axis and the horizontal line is the x-axis. The point of intersection between this line is called "Origin" and it's at the point (0,0).
There are four sections in a Coordinate plane which are called "Quadrants". See the drawing below to see their location in the Coordinate plane:
Having the point:
[tex](4,1)[/tex]You can notice that, the x-coordinate is positive and the y-coordinate is also positive. This means that the point (4,1) is located in the QUADRANT I.
Therefore, the answer is: b. I
Find the missing side of this righttriangle.19X16x = √ [?]
GIVEN:
We are given a right triangle with the sides labeled as indicated.
Required;
To find the value of the missing side, x.
Step-by-step solution;
For any right angled triangle, the value of a missing side can be calculated using the Pythagoras' theorem, provided the other two sides are given.
The theorem states thus;
[tex]\begin{gathered} c^2=a^2+b^2 \\ \\ Where; \\ c=hypotenuse,\text{ }a,b=other\text{ }sides. \end{gathered}[/tex]We can now substitute and solve as follows;
[tex]\begin{gathered} 19^2=x^2+16^2 \\ \\ 361=x^2+256 \\ \\ 361-256=x^2 \\ \\ 105=x^2 \end{gathered}[/tex]Now we take the square root of both sides and we have;
[tex]\begin{gathered} \sqrt{105}=\sqrt{x^2} \\ \\ x=\sqrt{105} \end{gathered}[/tex]Therefore;
ANSWER:
[tex]x=\sqrt{105}[/tex]Vega swam her leg of the race in 27.98 seconds and Janice swam her leg of the relay race in 25.679 seconds. What was their combined time for their part of the relay?A.2.301 secondsB.28.477 secondsC.53.669 secondsD.53.659 seconds
To get their combined time, get the sum of Vega's time and Janice's
[tex]27.98\text{ sec}+25.679\text{ sec }=53.659\text{ sec}[/tex]Therefore, their combined time for their part of the relay is 53.659 seconds.
Chang bought a bumper marked up 15.2% based on selling price at a local auto shop. If the markup is $39.91, find the selling price and the cost. Round to the nearest cent or tenth of a percent.
Answer:
cost price = $262.57
selling price = $302.48
Explanation:
The selling price is
Selling price = cost + markup
We know that markup is 15.2% of the cost price. Since the markup is $39.91,
[tex]\frac{15.2}{100}(\text{cost price)=39.91}[/tex][tex]0.152(\text{cost price) =39.91}[/tex]dividing both sides by 0.152 gives
[tex]\text{cost price}=\frac{39.91}{0.152}[/tex][tex]\boxed{\text{cost price}=\$262.57.}[/tex]The selling price is
cost price + 15.2% of the cost price
= (100% + 15.2%) cost price
=115.2% cost price
Now, 115.2% of the cost price is
[tex]\frac{115.2\%}{100\%}(262.57)[/tex][tex]=1.152(262.57)[/tex][tex]=\$302.48[/tex]Hence the selling price is $302.48.
Therefore, to summerise,
cost price = $262.57
selling price = $302.48
Which quadratic expression is written in standard form? -X2 - 5x + 7 0 ) (x + 3)x (x + 4)2 x² + 2(x+3)
Because the general expression for a quadratic equation is
[tex]ax^2\text{ + bx + c }[/tex]8. Write an inequality to represent the following constraint.Mowing a large yard (x) uses 0.3 gallons of gasoline, and mowing a small yard (y) uses 0.2 gallons of gasoline. There are 6 gallons of gasoline available. ______ ≤ _______
Answer:
0.3x + 0.2y ≤ 6
Explanation:
If mowing a large yard uses 0.3 gallons of gasoline, mowing x large yards will use 0.3 times x gallons of gasoline which can be written as
0.3x
In the same way, if mowing a small yard uses 0.2 gallons of gasoline, mowing y small yards use 0.2 times y gallons of gasoline which can be written as
0.2y
Therefore, the total gallons of gasoline will be
0.3x + 0.2y
However, this has to be less than or equal to 6, then
0.3x + 0.2y ≤ 6
please help I dont understand this I think you have to find the value for "?"
Answer:
8'' x 10''
Step-by-step explanation:
. Name a specific real-life model of a periodic function and a logisticfunction. List 2-3 defining characteristics or features of each type and describe howyour model or example displays those characteristics or features. State the domain andrange of each example you provide. Make sure your examples are functions!
Given:
Data is given
Required:
To state domain
Explanation:
Example: y=sinx
it is periodic function
its periods is 22
[tex]domain\text{ \lparen-}\infty\text{ , +}\infty)[/tex]range(-1,1)
Required answer:
above analysis
A scientist is studying the relationship between amiet temerature and the heights of individuals plants. When the ambient temperatures was 25 degree celsius plants reached maximum heights of 4.9 metters and when the ambient temperatures was 30 degrees Celsius plants reached maximum heights of 4.4 metters. What function best captures this relationship where x is temperature, in degrees Celsius and f(x) is plants height in meters
A function that describes relationship between Amite temperature and the heights of individuals plants is:
f(x) = -0.08x + 4.9
where, x is temperature, in degrees Celsius and f(x) is plants height in meters
In this question, we have been given a scientist is studying the relationship between Amite temperature and the heights of individuals plants.
When the ambient temperatures was 25 degree Celsius plants reached maximum heights of 4.9 meters
and when the ambient temperatures was 30 degrees Celsius plants reached maximum heights of 4.4 meters.
We need to find a function that describes this relationship where x is temperature, in degrees Celsius and f(x) is plants height in meters.
The rate of change in the height of plants.
Consider points (25, 4.9) and (30, 4.4)
r = (4.4 - 4.9) / (30 - 25)
r = -0.4 / 5
r = -0.08
So, a linear function in slope-intercept form would be,
f(x) = -0.08x + b
for x = 25,
2.9 = -0.08(25) + b
b = 2.9 + 2
b = 4.9
so, we get a linear function
f(x) = -0.08x + 4.9
Therefore, a function that describes relationship between Amite temperature and the heights of individuals plants is:
f(x) = -0.08x + 4.9
where, x is temperature, in degrees Celsius and f(x) is plants height in meters
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i need to know what to do, I don’t know if I need to make an equation or I just need to divide something…
Solution:
Let x be the number of 4-player games and y be the number of 2-player games played, such that;
[tex]\begin{gathered} x+y=10........equation1 \\ \\ 4x+2y=32.........equation2 \end{gathered}[/tex]From equation1;
[tex]x=10-y.................equation3[/tex]Substitute equation3 in equation2;
[tex]\begin{gathered} 4(10-y)+2y=32 \\ \\ 40-4y+2y=32 \\ \\ 40-32=4y-2y \\ \\ 2y=8 \\ \\ y=4 \\ \end{gathered}[/tex]Substitute the value of y in equation 3;
[tex]\begin{gathered} x=10-4 \\ \\ x=6 \\ \end{gathered}[/tex]ANSWER: Six 4-player games and four 2-player games were played.
What is the cardinality of the set {2, {3}}?
Given,
The set is {2, {3}}.
The cardinity of the set is the number of elements in the set.
Consider,
A = {2, {3} }
The cardinity of the set is,
[tex]|A|=2[/tex]Hence, the cardinality of the set is 2.
If x is 3 what is there value of 4x^2 - 5
To evaluate the given at x = 3, substitute x by 3, and evaluate the expression accordingly
[tex]\begin{gathered} 4x^2-5 \\ =4(3)^2-5 \\ =4(9)-5 \\ =36-5 \\ =31 \end{gathered}[/tex]Therefore, the value of the given at x = 3, is 31.
Use multiplication properties to find the product. 3 x (3 x 7) =
The given expression is
3(3 * 7)
The multiplication properties include
1) Commutative property: When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands.
This means that
3 * 7 = 7 * 3 = 21
3 * 21 = 63
2) associative property.: when 3 or more numbers are multiplied, the product is the same regardless of the grouping of the factors. This means that
3(3*7) = 7(3 * 3) = 3(7 * 3) = 63
b)
(7x 10¹) + (5x 10³)
Answer:
5.07*10³
Step-by-step explanation:
Write in standard form and then add.[tex]\sf 7*10^1 + 5*10^3 = 70 + 5* 1000[/tex]
= 70 + 5000
= 5070
Now, again write in scientific notation.[tex]\sf 5070 = 5.07 * 10^3[/tex]
Is the graph above discrete or continuous?What are the domains of the graph?
Answer:
Continuous graph.
[tex]\text{Domain: }(-\infty,\infty)[/tex]Explanation:
Looking at the graph in the picture, we can say that it is a continuous graph because the line of the graph is continuous and not interrupted. There is a y value for every value of x.
The domain of the function graphed in the image is all real numbers which can be represented as shown below;
[tex]\text{Domain: }(-\infty,\infty)[/tex]Laith GhannoomConfidence intervals for MeansMay 09, 10:06:04 PMA study by the department of education of a certain state was trying todetermine the mean SAT scores of the graduating high school seniors.The study examined the scores of a random sample of 51 graduatingseniors and found the mean score to be 512 with a standard deviationof 109. Determine a 95% confidence interval for the mean, rounding allvalues to the nearest tenth.Submit Answer
Confidence interval of the mean.
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=512.
The sample size is N=51.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{109}{\sqrt{51}}=\dfrac{109}{7.141}=15.263[/tex]The degrees of freedom for this sample size are:
[tex]df=n-1=51-1=50[/tex]The t-value for a 95% confidence interval and 50 degrees of freedom is t=2.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2\cdot15.263=30.526\approx30.5[/tex]Then, the lower and upper bounds of the confidence interval are:
[tex]\begin{gathered} LL=M-t\cdot s_M=512-30.5=481.5 \\ UL=M+t\cdot s_M=512+30.5=542.5 \end{gathered}[/tex]Answer: The 95% confidence interval for the mean is (481.5, 542.5).
list three terms that are like the given term -19m
Like terms are terms that have the same variables and powers. The coefficients do not need to match.
Then, in this case, three terms that are like -19m:
1. 7m
2. -12m
3. 9m
In a class of students, the following data table summarizes how many students have acat or a dog. What is the probability that a student who does not have a dog has a cat?Has a cat Does not have a catHas a dog912Does not have a dog35
we have that
total students does not have a dog=8
so
the probability is
P=3/8At State College last term, 70 of the students in a Physics course earned As, 99 earned Bs, 110 got Cs, 99 were issued Ds, and 54 failed the course. If this grade distribution was graphed on a pie chart, how many degrees would be used to indicate the C region?Round your answer to the nearest whole degree.
Notice that 110 students out of the total number of students is the same as the number of degrees we are looking for out of 360 degrees.
Now, the total number of students is:
[tex]70+99+110+99+54=432.[/tex]Then, if x is the number of degrees that we are looking for, we can set the following equation:
[tex]\frac{x}{360}=\frac{110}{432}\text{.}[/tex]Multiplying the above equation by 360 we get:
[tex]\begin{gathered} \frac{x}{360}\times360=\frac{110}{432}\times360, \\ x=91.666667\approx92. \end{gathered}[/tex]Answer: 92 degrees.
Graph h(x) = 33(1.45)*. What is the constant percent rate of change of f(x) with respect to x? Does the graph show growth or decay?
45% growth
45% decay
55% growth
55% decay
The constant percent rate of change of the function is option (a) 45% growth
The constant percent rate of change of the functionThe equation of the function is given as
f(x) = 33(1.45)^x
The above function is an exponential function
An exponential function is represented as
y = ab^x
Where b represents the growth or decay factor
So, we have
b = 1.45
We can see that the value of b is greater than 1
This means that the graph would represent a growth
The percent rate of change is then calculated as
Rate = b - 1
This gives
Rate = 1.45 - 1
Evaluate
Rate = 0.45
Rewrite as
Rate = 45%
Hence, the rate of change is 45% growth
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Answer:
A) 45% growth !!!
Step-by-step explanation:
i took the test
find the missing term that completes the square of a² + 4a
Answer:
4
Explanation:
Given the expression:
[tex]a^2+4a[/tex]To complete the square:
First, identify the coefficient of a.
• The coefficient of a = 4
Next, divide the coefficient by 2 and square it.
[tex]\begin{gathered} \frac{4}{2}=2 \\ 2^2=4 \end{gathered}[/tex]Thus, the missing term that completes the square of a² + 4a is 4.