Joshua's 15 ft ladder, if leaned against the wall to reach a height of 14.8 ft, would be at an unsafe angle less than 70° and thus, is not safe to use in this manner.
Explanation:The student has asked whether Joshua's ladder, which is 15 feet long and is supposed to lean against a wall with the top at 14.8 feet above the ground, will be safe with an angle no greater than 70°. To determine this, we can use the trigonometric function cosine, which relates the adjacent side (the height at which the top of the ladder reaches the wall) to the hypotenuse (the length of the ladder) in a right-angled triangle. The cosine of the maximum safe angle (70°) should therefore be equal to or greater than the ratio of the height of the ladder against the wall (14.8 feet) to the length of the ladder (15 feet).
We calculate the cosine of 70°: cos(70°) ≈ 0.342. Then we calculate the ratio 14.8/15 which equals 0.9867. Since 0.9867 is much greater than 0.342, it means the ladder will form an angle that is less than 70°, which is not within the safe range as per Joshua's requirement.
Therefore, it is not safe for Joshua to lean the ladder in this manner because the angle formed will be steeper than the maximum safe angle of 70°, which may result in the ladder slipping.
7s-9=5 How do I get my answer?
Answer:
s = 2
Step-by-step explanation:
You want to isolate the variable so add 9 to both sides. That gives you 7s = 14. Now divide both sides by 7 to get s alone, and that equals s = 2. I hope this helps and please mark me brainliest!
Answer:
[tex]s = 2[/tex]
Step-by-step explanation:
[tex]7s - 9 = 5 \\ add \: 9 \: from \: both \: sides \\ \\ 7s = 14 \\ divide \: both \: sides \: by \: 7 \\ \\ s = 2[/tex]
Simplify (1 − sin x)(1 + sin x). (2 points)
a
1
b
cos2 x
c
sin2 x
d
tan2 x
Answer:
cos²x
Step-by-step explanation:
(a-b)(a+b)=a²-b²
sin²x+cos²x=1 => cos²x=1-sin²x
(1 − sin x)(1 + sin x)=1-sin²x=cos²x
The simplified value of the (1 − sin x)(1 + sin x) is cos² x.
The correct option is B.
To simplify the expression (1 − sin x)(1 + sin x), we can use the identity for the difference of squares, which states that (a − b)(a + b) = a² − b².
So, it can written as
(1 − sin x)(1 + sin x) = (1)² − (sin x)².
Now, using the identity sin² x + cos² x = 1, we can substitute (sin x)² with (1 − cos² x):
(1)² − (sin x)² = 1 − (1 − cos² x) = 1 − 1 + cos² x = cos² x.
Therefore, the simplified expression is cos² x.
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Which graph shows a system of equations with exactly one solution?
Answer:
d
Step-by-step explanation:
The graph that shows a system of equations with exactly one solution is graph d
Which graph shows exactly one solution?From the question, we have the following parameters that can be used in our computation:
The graphs
The graph that shows a system of equations with exactly one solution is the graph where there is only one point of intersection on the functions
Using the above as a guide, we have the following:
The graph that shows exactly one solution is (d)
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graph the solutions of the inequality on a number line. describe the solution to the inequality.p>4
I really need help with this question.
Answer:
I got 4/5
Step-by-step explanation:
Evaluate sin 5pi/4
Thank you
Answer:
-sqrt(2)/2
Step-by-step explanation:
5pi/4 lies in the third quadrant with basic angle: 5pi/4 - pi = pi/4
sin(pi/4) = sqrt(2)/2
Since it's in quadrant 3, sin would be negative
sin(5pi/4) = -sqrt(2)/2
sqrt: square root
When the above math expression is evaluated, the value of sin(5π/4) is -√2/2.
How is this so?
To evaluate sin(5π/4), we can use the unit circle or trigonometric identities.
The angle 5π/4 is located in the third quadrant of the unit circle, where the sine function is negative.
In the unit circle, at 5π/4, the corresponding point is (-√2/2, -√2/2). The y-coordinate of this point represents the value of the sine function.
Therefore, sin(5π/4) = -√2/2. hence, the value of sin(5π/4) is -√2/2.
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A bank loans a stylist $7,500 for 1 year at an interest rate of 6% per year to purchase a car. What is the yearly interest payment?
Answer:
450
Step-by-step explanation:
7500 times 6% is 450 your equation will be PRT principal which is the amount you started with times rate which is the % times time in years
Which set of measurements will form a unique triangle?
angle measures of 45°, 45°, 90°
angle measures of 60°, 60°, 60°
side measures of 1 cm, 1 cm, 100 cm
side measures of 20 cm, 20 cm, 20 cm
Answer:
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Take the first two numbers (60 and 60) and add them, then compare it to the last number (60). If the answer from adding is greater than the 3rd number, you have your answer :) Hope this helps!
The table shows the results of a survey of students in two math classes. Find P(more than 1
hour of TV | 6th period class). Round to the nearest thousandth.
Did You Watch More Than One Hour of TV Last Night?
Answer:
0.545
Step-by-step explanation:
In the missing table the following information is shown:
Did You Watch More Than One Hour of TV Last Night?
3rd Period Class: Yes- 11 No- 6
6th Period Class: Yes- 12 No- 10
The probability that the student watched more than 1 hour of TV given that he/she belongs to 6th period class is:
P(more than 1 hour of TV | 6th period class) = 12/(12+10) = 0.545
The probability (more than thanhour of TV | 6th period class).and rounded to the nearest thousandth is:
0.545What is Probability?This refers to the chance occurrence of an event based on both dependent and independent variables.
Hence, from the complete question, there is the table which gives the following data;
Did You Watch More Than One Hour of TV Last Night?3rd Period Class: Yes- 11 No- 66th Period Class: Yes- 12 No- 10Hence, the probability that the student watched more than 1 hour of TV given that he/she belongs to 6th period class is:
= 12/(12+10) =
0.545
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Billy collects marbles. Each marble in his collection weighs about 4 ounces. His collection weighs about 20 pounds in all. About how many marbles are in his collection?
Which is the graph of y = cos(x) + 3?
Answer:
(the image attached)
Step-by-step Explanation:
Amplitude: 1
Period: 2π
Phase Shift: 0 (0 to the right)
Vertical Shift: 3
An image is attached below for the graph of the function y = cos(x) + 3
What are trigonometric functions ?A function such as the sin, cos, tan, cot, sec, and cosec of an angle or an arc expressed in terms of the ratios of pairs of sides of a right angled triangle.
The graph of cos(x) is a periodic function with time period 2π. After every 2π it repeats itself so we call it as a periodic function.
for x = 0
y = cos(0) + 3
y = 1 + 3
y = 4
for x = π/2
y = cos(π/2) + 3
y = 0 + 3
y = 3
An image graph of cos(x) + 3 is given try out different vales of x to understand more about how the function behaves.
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In ΔGHI, the measure of ∠I=90°, HI = 3 feet, and IG = 2.3 feet. Find the measure of ∠H to the nearest degree.
Answer:
37
Step-by-step explanation:
Answer:
37
Step-by-step explanation:
37.476 = 37
Jason is a very good bowler and has proven over the
course of a season of league play that he gets a
STRIKE 50% of the time. Using this empirical
probability what is the probability that Jason will get
exactly 7 strikes out of 10 attempts?
Answer:
The probability that Jason will get exactly 7 strikes out of 10 attempts is 0.117.
Step-by-step explanation:
We are given that Jason is a very good bowler and has proven over the course of a season of league play that he gets a STRIKE 50% of the time.
Also, Jason has been given 10 attempts.
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......[/tex]
where, n = number trials (samples) taken = 10 attempts
r = number of success = 7 strikes
p = probability of success which in our question is % of the time
he gets a strike, i.e; p = 50%
Let X = Number of strikes Jason get
So, X ~ Binom(n = 10, p = 0.50)
Now, probability that Jason will get exactly 7 strikes out of 10 attempts is given by = P(X = 7)
P(X = 7) = [tex]\binom{10}{7} \times 0.50^{7} \times (1-0.50)^{10-7}[/tex]
= [tex]120 \times 0.50^{7} \times 0.50^{3}[/tex]
= [tex]120 \times 0.50^{10}[/tex]
= 0.117
Therefore, the probability that Jason will get exactly 7 strikes out of 10 attempts is 0.117.
The probability that Jason will get exactly 7 strikes out of 10 attempts can be calculated using the binomial probability formula with a 50% strike rate.
The probability that Jason will get exactly 7 strikes out of 10 attempts, given a 50% strike rate, can be calculated using the binomial probability formula:
P(X = k) = C(n, k) * p[tex]^{(k)}[/tex] * (1 - p)[tex]^{(n - k)}[/tex]
n = number of trials (10)k = number of successful trials (7)p = probability of success (0.5, or 50%)Using the formula, we get:
P(X = 7) = C(10, 7) * (0.5)⁷ * (0.5)⁽¹⁰⁻⁷⁾
Calculating the combination C(10, 7) and following the formula yields the specific probability value for Jason to get exactly 7 strikes in 10 attempts.
Marty bought a shirt for $9.50, sandals for $15.50, shorts for $11.75, and sunscreen for $5.25. Use mental math to find the total amount he spent. Explain.
Answer:
42
Step-by-step explanation:
9.5+15.5=25. 11.75+5.25=17. 25+17=42. That should explain it. I hope this helps.
Answer:
Marty spent $42. How I got this answer is I added 11.75+5.25 first, equaling 17. Then I added 15.50 to 17, equaling 32.50. Finally I added 9.50 to 32.50 equaling 42.
Step-by-step explanation:
9.50+15.50+11.75+5.25= $42
Is (2,2) in the solution set of y ≥ 9x - 8?
The cost of a ball is $0.58. David pays for the ball with
a $1 bill. How much change should David get back?
A $0.42
B $0.43
C $0.52
D $1.58
Answer:
A
Step-by-step explanation:
It's A just trust me I'm not doing the work lol
Answer:
The answer would be A. $.042
Step-by-step explanation:
For you to find out the answer to how much change he should get back, subtracting the two numbers will get you the answer
1.00 - .58 = .42
Feel free to let me know if you need more help. :)
PLEASE HELP
Find the surface area of a triangular prism, base measures 6 cm, height measures 4 m, sides measure 5 cm and height of prism measures 10 cm
Answer:
v=99.215674164922cm^2
I NEED HELP ASAP RIGHT NOW NOW NOW
Answer:
2^120
Step-by-step explanation:
6 x 20 = 120
Answer:
4²⁶
Step-by-step explanation:
It's easier than you think; all you need to do is multiply 2⁶ x 2²⁰.
Multiply the bases and add the exponents. You will get 4²⁶.
Marya plans to participate in a 20 km walk-a-thon. To prepare, she walked 4 km on Monday. She plans to increase her walk by 2 km each week until she reaches 20 km. Marya’s calculations: 4 + 2 = 6. 6 + 2 = 8. 8 + 2 = 10. 10 + 2 = 12. 12 + 2 = 14. 14 + 2 = 16. 16 + 2 = 18. 18 + 2 = 20. The equation representing Marya’s calculations is 4 + 2 w + 20. How many weeks will it take Marya to reach her goal of a 20 kilometer walk? 8 9 10 12
Answer: 8 weeks
Step-by-step explanation:
20 - 4 = 16
16 / 2 = 8
The correct answer is 8 weeks.
In the equation, t is a constant. If the equation has no real solutions, what could be the value of t?
2x2 − 4x = t
A) −3
B) −1
C) 1
D) 3
Answer:
t = - 3
Step-by-step explanation:
2x2 - 4x = t
2x2 - 4x - t = 0
a = 2, b = - 4, c = - t
b2 - 4ac = 0
(-4) - 4(2)(-t) = 0
16 + 8t = 0
8t = - 16
t = - 3
good day, and be safe
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Solve for x
9(x+1)=25+x
Answer:
x = 2
Step-by-step explanation:
9(x+1) = 25+x
Distribute
9x +9 = 25+x
Subtract x from each side
9x-x +9 = 25+x-x
8x +9 = 25
Subtract 9 from each side
8x+9-9 = 25-9
8x = 16
Divide each side by 8
8x/8 = 16/8
x = 2
Given the following exponential function, identify whether the change represents growth or decay, and
determine the percentage rate of increase or decrease. y=3400(1.97)^x
Answer: 97% growth rate.
Step-by-step explanation:
Hi, to answer this question we have to analyze exponential function:
A = P (1 + r) t
Where:
p = initial value
r = growth or decay rate (decimal form)
t= number of time intervals
A = value after t intervals
Replacing with the values given:
y=3400(1.97)^x
Where the term 1.97 = 1 + r
Solving for r:
1.97-1 = r
0.97 =r
Since the rate is positive, it is a growth rate.
To determine the percentage we have to multiply it by 100
0.97 x 100 = 97%
Feel free to ask for more if needed or if you did not understand something.
Sara goes shopping with $100 at the mall and she used th
calculate the amount of change she should receive. How
the end of the day?
100 - (12 + 17 + 7 + 2(4) + 3(5) + 4)
$37
$0
$42
$21
Answer:
$37
Step-by-step explanation:
2x4=8
3x5=15
12+17+7+8+15+4=63
100-63=37
$37
Answer:37
Step-by-step explanation: 12+17=29 29+7=36 36+8=44 44+15=59 59+4=63 And you 2(4) you multiply and 3(5) you also multiply
Then you subtract 100 and 63and get 37
Which choices are equations for the line shown below? Check all that apply.
A. y = 2x + 1
B. y = -0.5x + 1
C. y - 5 = -2(x+2)
D. y + 3 = -2x(x+2)
F. y = -2x + 1
Answer:
B and F
Step-by-step explanation:
it is a negative line and has a y intercept of 1
Answer: F | C | D
Step-by-step explanation: Because Im goated with the sauce
whats 25 times 25% :)
Answer:
the answer is in the
Step-by-step explanation:
Answer:
6.25
Step-by-step explanation:
Check all of the following that are proper units for measuring length in the
U.S. system of units.
A. Grams
B. Feet
C. Inches
D. Kilometers
Answer:
all except kilometers
Step-by-step explanation:
Find the best buy (based on price per unit) for cereal.
18-ounce size: $4.79
21-ounce size: $3.89
32-ounce size: $6.49
The best buy for cereal is the 21-ounce size as it costs $0.185 per ounce, which is cheaper compared to the 18-ounce size ($0.266 per ounce) and the 32-ounce size ($0.203 per ounce).
Explanation:To determine the best buy for cereal, we first need to calculate the price per ounce for each size. The formula to calculate is Price per Ounce = Total Price / Ounce Size. Using this formula, let's calculate for each cereal pack:
18-ounce size: $4.79/18 = $0.266 per ounce 21-ounce size: $3.89/21 = $0.185 per ounce 32-ounce size: $6.49/32 = $0.203 per ounce.
Based on these calculations, we see that the 21-ounce size cereal pack is the best buy, as it offers the lowest price per ounce.
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A political scientist has 12 volunteers for a political opinlon survey. The political scientist selects 2 of the volunteers to
complete different variations of the survey. How many ways can this be done?
132
144
169
196
Find the length of the second base of a trapezoid
with one base measuring 15 feet, a height of
7.6 feet, and an area of 98.8 square feet.
A. 9 ft
B. 10 ft
C. 11 ft
D. 12 ft
Answer:
11 ft
Step-by-step explanation:
The area of a trapezoid is given as:
A = ½(a + b)h
Where a = length of one base of the trapezoid = 15 ft
b = length of the second base of th trapezoid
h = height of the trapezoid = 7.6 ft
When the area is 98.8 ft², the length of the second base will be:
98.8 = ½(a + 15) * 7.6
2 * 98.8 = (a + 15) * 7.6
197.6 / 7.6 = (a + 15)
26 = (a + 15)
=> a = 26 - 15 = 11 ft
The length of the second base if the trapezoid is 11 ft.
Identify the slope and y-intercept of the line given by the equation: y = 2x + 1.
Answer:
The slope is 2 and the y-intercept is 1 (hope this helped!)
Slope = 2, y-intercept = 1
What is intercept form of line?An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
Given equation of line
y = 2x+1
comparing it with standard intercept equation of line
y = mx+c
where m is slope and c is the y-intercept.
Slope m = 2
Y- intercept c = 1
Hence, the slope and y- intercept of the line are 2 and 1 respectively.
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